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A Novel Unsupervised Neuro-Fuzzy System Applied to Circuit Analysis

Hadi Sadoghi Yazdi Seyed Ebrahim Hosseini

Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

E-mail: {sadoghi, ehosseini}@sttu.ac.ir

Abstract: In this paper, for the first time, unsupervised neuro-fuzzy system is presented and is applied in circuit analysis. Usually Neuro-fuzzy systems have a learning phase in which the system is trained with input data. But if the training set is unavailable, conventional procedures encounter serious problem. Due to unsupervised character, no learning data is needed. To investigate the method, linear circuit is analyzed. Results are compared with the exact solution.

Keywords: Unsupervised neuro-fuzzy system, Circuit analysis.

1. Introduction Artificial neural networks (ANN), as intelligent

computational tools have been used for modeling and optimization of analog circuit design [1]. For example optimization of high-speed very large scale integration (VLSI) interconnects [2], global modeling [3, 4] and circuit synthesis [5]. Numerous problems in science and engineering can be converted to a set of differential equations. Basic numerical methods can be used to solve differential equations such as the finite difference method, the finite element method, the finite volume method and the boundary element method.

Neural networks (NNs) are used to approximate stochastically unknown functions and relations. This approximation is a kind of implicit model of the unknown dependencies. In contrast, differential equations are used to model explicitly all relations. Solving ordinary and partial differential equations can be learned to a good degree by an artificial neural network. The basic ideas were presented by Lagaris, Likas, and Fotiadis [6]. Let the differential equation to be solved be given by:

( ) ( ) ( )( ) ,0,...,,, 2 nRDxxxxxG ⊆∈=∇∇ ψψψ (1)

Where ( )xψ denotes the solution, G is the functional defining the structure of the differential equation, and ∇ is some differential operator. The basic idea, called collocation method, is to discretize the domain D over a finite set of points D . Thus (1) becomes a system of equations. Suppose an approximation of the solution ψ(x) is given by the trail solution ψt(x). As a measure for the degree of fulfillment of the original differential equation (1), an error function similar to the mean squared error is defined:

( )[ ] .,...,,,1 22∑∈

∇∇=Dx

tttit

xGD

E ψψψ (2)

Therefore, finding an approximation of the solution of (1) is equal to finding a function that minimizes the error E . It is well known that a multilayer feed forward neural network is a universal approximator [7], therefore the trail solution ψt(x) can be represented by such an artificial neural network. In case of a given network architecture the problem is reduced to finding a configuration of weights that minimizes (2). As E is differentiable with respect to the weights for most differential equations, efficient gradient-based learning algorithms for artificial neural networks can be employed for minimizing (2).

Intelligent Systems Scientific Society of IranIntelligent Systems Scientific Society of Iran

First Joint Congress on Fuzzy and Intelligent SystemsFerdowsi University of Mashhad, Iran

29-31 Aug 2007

1 ، دانشگاه فردوسي مشهد ، دانشگاه فردوسي مشهد13861386 شهريور شهريور 77--99 ، ، فازيفازيتمين كنفرانس سيستمهاي تمين كنفرانس سيستمهاي ففهه

A Numerical Approach Based on Neuro-Fuzzy Systems for Obtaining Functional Inverse

Hadi Sadoghi Yazdi1, Sohrab Effati2

1-Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

2-Department of Mathematics, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

Abstract: In this paper, a new and easy available numerical method is presented in calculation of functional inverse. As for ANFIS (Adaptive Network based Fuzzy Inference System) model is available without great difficulty in MATLAB software also due to important of obtaining functional inverse in wide range applications, we present ANFIS-based approach for the first time for obtaining inverse of mathematical functions. The proposed approach includes two main stages, in the first step; some limited points are sampled from desired function using Monte Carlo simulation and second step contains training of ANFIS system that input system is output points of function and ANFIS desired values are input values to function. One of notes in the proposed approach is calculation of inverse of time varying functions only with tuning of generated fuzzy model with the least square and the back propagation (BP) algorithms to form of hybrid learning algorithm which able into tracking of time varying functions. Experimental results over many functions show superiority of the proposed method relative MATLAB software. Keywords: Functional inverse; Adaptive Network based Fuzzy Inference System; Monte Carlo method; Hybrid learning; MATLAB software. 1. Introduction

Functional inverse not only is used in mathematics but also have many applications in engineering and sciences. Finding sources from measured data is a common problem in a real world. From the mathematic point of view, solving the equation obtain inverse of function or an iterative approach give us functional inverse. If f is a continuous function

defined in interval [ ]ba, , g is inverse of f if

( )( ) xxgf =o or ( )( ) xxgf = ; so g is 1−f or is a functional inverse. Functional inverse can study from different views: Finding source of generated data:

The inverse problem of finding the source from the data is other form of functional inverse. In practice a process has two elements, the physical process and the measurement. In the measurement procedure noise is inserted to data. So it is needed a smoother is selected for noise reduction then backward mapping is required for finding source [1].

In the field of image processing, finding main image from degraded image is based on dealing with the problem as an inverse problem. Based on the observation model, our objective is to obtain a high

resolution image which is as close as possible to the original high resolution image subject to certain constraints [4].

Inverse learning in signal processing:

The developments of inverse learning was initiated from adaptive signal processing and control of linear systems approach [2, 3] and due to its potential applicability, until now several modifications and applications are still being developed in the literature.

In data communications, receiver equalization has become an essential building block to mitigate the inter-symbol interference problem, which is due to limited bandwidth of low cost channel materials. Several equalization methods have been developed which are types of functional inverse [5].

Constructing inverse signal:

Creating of inverse signal for reducing of undesirable signal is another view of functional inverse. Active noise control systems are based on the principle of superposition: an unwanted noise is cancelled out by the action of a secondary noise that generates a sound wave of equal amplitude and opposite phase [6]. This idea has evolved and new applications have been developed in which the


29-31 Aug 2007 Intelligent Systems Scientific Society of IranIntelligent Systems Scientific Society of Iran


Improved Genetic Algorithm-Based Optimization of Fuzzy Logic Controllers

Amin Chegeni, Abdollah Khoei, Khayrollah Hadidi

Microelectronics Research Laboratory Urmia University

[email protected] [email protected]

[email protected] Abstract: This paper presents a new method to improve genetic algorithm-based optimization of fuzzy logic controllers considering both membership functions and rules. We indicate that eliminating the limitation on symmetric membership functions and rules results better optimization. Furthermore, we optimize fuzzy logic controller using genetic algorithm considering whole of system states, which cause the reliability of the controller to improve significantly. Keywords: Fuzzy logic controller, genetic algorithm, optimization. 1 Introduction In the last decade, many researches have focused on the learning and tuning algorithms for both model based and model-free design of fuzzy logic controllers (FLCs). The literature report successful applications of methods based on fuzzy clustering, neural networks (NNs), reinforcement learning, and genetic algorithms (Gas) for the most widely adopted techniques. In many researches, only membership functions (MFs) are used in the optimization process, and in some of them, both MFs and rules are optimized. However, two important points usually are not considered in the practical optimization. First, in almost all articles, the resulted MFs and/or rule-table are constrained to be symmetrical [1, 3, 4, 5]. Considering that the plant controlled by FLC is generally nonlinear, the optimal MFs and rule table are not necessarily symmetrical; therefore, restricting the optimization to symmetric results decreases the

degree of freedom and degrades the performance. Second, since the plant is nonlinear, as we will explain in this paper, if the FLC is optimized for a special input signal, the system may be unstable for other inputs. Thus, optimizing the FLC for only one special input is a faulty optimization. In this paper, we indicate that eliminating the mentioned limitation on symmetric MFs and rule table results in more degree of freedom and consequently better optimization. Furthermore, we analyze the effect of optimizing FLC for different states of the system, and show that the reliability of the controller improves significantly when involving more states of the system in the optimization. This paper is organized as follows. In section II, a brief description of GA is presented. Optimization mechanism will be presented in section III, and in section IV, two well-known examples along with their simulation results will be presented to verify the feasibility and advantage of this method. Section V concludes this work. 2 Genetic Algorithms (GA’s) GA’s are search algorithms modeled after the mechanics of natural genetics [8]. They are useful approaches to problems requiring effective and efficient searching, and their use is widespread in applications to business, scientific, and engineering fields. In an optimally designed application, GA’s can be used to obtain an approximate solution for single variable or multivariable optimal problems. Before a GA is



29-31 Aug 2007


FUZZY REAL NUMBERS AND THEIR RELATION TO THE TOPOLOGICAL VECTOR SPACE

Abstract: : In this paper first we show that the fuzzy normed spaces (FNS) constructed by fuzzy real numbers are topological vector space, and then we prove that the definition of fuzzy continuity and topological continuity are equivalent. By using that we can easily establish all results in the topological vector spaces for the fuzzy normed spaces.. Keywords: Fuzzy real number, Fuzzy norm, Fuzzy bounded operator, topological vector space. 1 Introduction Felbin [1] put forward the concept of a fuzzy normed linear space (briefly , FNS) by applying the notion of fuzzy distance to the linear space. It is more natural and practical that the norm of a point is a fuzzy number rather than a real number. Xiao and Zhu [2] investigated the linear topological structure and some basis properties of FNS under the condition of weaker right norm and left norm. We will show that a fuzzy normed space is also a topological vector space and we will prove that the fuzzy continuity and topological continuity (fuzzy boundedness and topological boundedness) are equivalent. So all results and theorems in the topological vector spaces hold for the fuzzy normed spaces in general. There are many important known theorems in the topological vector spaces; among them are Uniform boundedness, Open mapping theorem, Closed Graph theorem, Han-Banach theorem,... which remain true for fuzzy normed spaces. Therefore as it is cited above already proven in classical analysis, for fuzzy normed spaces. The only problem remain is that we investigate the properties in fuzzy normed spaces which does not hold in classical analysis. 2 preliminaries Our notation and definition follow [2].

We denote the origin of a linear space by θ; and the set of all fuzzy real number by F. If h∈ F and h(t) = 0 whenever t < 0, then h is called an non-negative fuzzy real number and by F+ we mean the set of all non-negative fuzzy real number. The number 0 stands for the fuzzy number satisfying 0 (t) = 1 and 0 (t) = 1 if t ≠0 clearly, 0 ∈ F+. The set of all real numbers can be embedded in F because if r ∈ (-∞ , ∞), then r ∈ F satisfies r (t) =

0 (t - r). For h ∈ F , r ∈ (0,∞) and α∈ (0,1], r • h

is defined as (r • h)(t) = h(t/r) and 0 • h is defined to be 0 ; the α-level set [h]α = {t : h(t) ≥ α} is a closed interval and we denote it by [h]α= [h −

α ,h +α ].

Definition 2.1. Let X be a linear space over real number field; L and R (respectively, left norm and right norm) be symmetric and non decreasing mapping from [0, 1] × [0, 1] into [0,1] satisfying L(0,0) = 0 , R(1,1) = 1. Then ∥ .∥ is called a fuzzy

norm and (X, ∥ .∥ , L , R ) a fuzzy normed space

(abbreviated to FNS). If the mapping ∥ .∥ from X into F+ satisfies the following axioms where [∥ x∥ ]α = [∥ x∥ −

α ,∥ x∥ +α ] for x∈ X and

α∈ (0,1] )

I. SADEQI AND M. SALEHI [email protected]



29-31 Aug 2007


Fuzzy Seminormed Linear Space

Abstract: In this note we introduce and study the notion of fuzzy seminorm and we get some new results. Finally we give an example of a fuzzy seminorm space which is fuzzy normable but is not classical normable. Keywords: fuzzy normed space, fuzzy seminorm, Minkowski functional, fuzzy metric. 1 Introduction In 1984, Kastaras [3] first introduced the idea of fuzzy norm on a linear space. In 1992, Felbin [4] introduced an idea of a fuzzy norm on a linear space whose associated metric is Kaleva [5] type. In 1994, S.C.Chang and J.N.Mordeson [6] introduced an idea of a fuzzy norm on a linear space whose associated metric is Kramosil and Michalek type [7]. Following Chang and Mordeson, In 2003, T.Bag and S.K.Samanta introduced in [1] a definition of fuzzy norm and proved the decomposition theorem of fuzzy norm to a family of crisp norms. We introduce the fuzzy seminorm and study some of it's properties, then by an example we will show that a family of fuzzy seminorm implies a fuzzy norm on C (Ω ) space but it is not true in classical case. Preliminary Definition: [1] Let X be a vector space. A fuzzy subset N of X × ℜ is called a fuzzy norm on X if the following condition, are satisfied for all

x, y ∈ X and c ∈ ℜ : (N1) N(x, t) = 0 ; ∀ t ∈ ℜ with t ≤ 0 (N2) N(x, t) = 1 ; ∀ t∈ ℜ , t > 0 iff x=0 (N3) N(c x, t) = N(x, t/|c|), ∀ t∈ℜ , t >0 and c ≠ 0 (N4) N(x + y, t +s) ≥ min {N(x, s), N( y, t)}, for all x ,y∈ X , s ,t ∈ℜ

(N5) N( x , . ) is a non -decreasing function on ℜ , and lim N(x, t)=1 as t ∞→ . The pair (X, N) is said to be a fuzzy normed space.

2 Fuzzy seminorm

Definition: A fuzzy seminorm on a vector space X is a function on X × ℜ such that P1) ∀ t ∈ℜ with t ≤ 0, ρ (x, t) =0; P2) ∀ t∈ ℜ with t > 0, ρ (cx, t) = ρ (x, t/|c|) if c≠ 0 P3) ∀ t, s ∈ℜ , x, u ∈ X , ρ (x+u, t+s) ≥ min { ρ (x, t), ρ (u, s) } P4) ρ ( x , . ) is a non-decreasing function of ℜ and lim ρ (x, t)=1 as t ∞→ Note : A fuzzy seminorm ρ is a fuzzy norm N if it satisfies ; ρ (x, t)= 1 ∀ t∈ℜ with t > 0 then x = 0. Definition: A family P of fuzzy seminorms on X is said to be separating if to each x≠ 0 corresponds at least one ρ ∈ P and t∈ℜ such that ρ (x, t) ≠ 1. Theorem: Let ρ is a fuzzy seminorm on a vector space X. Define αρ (x) = inf { t : ρ (x ,t) ≥ α }, α ∈ (0,1). Then { })1,0(: ∈αρα an ascending

I . Sadeqi and F. Solaty kia [email protected]




A Novel Algorithm for Tuning of the Type-2 Fuzzy System

Sayed Mohammad Ali Mohammadi1 Ali Akbar gharaveisi1 Mashaalah Mashinchi2

[email protected] [email protected] [email protected] 1. Department of Electrical Engineering, Shahi Bahonar University of Kerman-Iran

2. Department of Mathematic, Shahi Bahonar University of Kerman –Iran

Abstract- Type-2 fuzzy logic systems (FLSs) let uncertainties that occur in rule-based FLSs be modeled using the new third dimension of type-2 fuzzy sets. Although a complete theory of type-2 FLSs exists for general type-2 fuzzy sets, it is only for interval type-2 fuzzy sets that type-2 FLSs are practical. Type 2 fuzzy sets allow for linguistic grades of membership. A type-2 fuzzy inferencing systems uses type-2 fuzzy sets to represent uncertainty in both the representation and inferencing. However; as with type-l fuzzy systems there is till an issue with regard to the design of the appropriate membership functions. One of the best performance the fuzzy inference system is optimized by the least square and numerical method .The key advantages of the least square method are the efficient use of samples and the simplicity of the implementation but it can be take long time for convergence. This paper presents a novel type-2 adaptive system for learning the membership grades of type-2 fuzzy sets which can be important. The results from the application problems lead us to believe that this approach offers the capability to allow linguistic descriptors to be learnt by an adaptive network and we can use some new algorithm same as Reinforcement Learning Methods for adaptation. Key word: Fuzzy Decision, Type 2 Fuzzy Sets, Adaptive Fuzzy Systems, FOU .

I. Introduction One possible approach to deal with the vague concepts is fuzzy logic systems, which are based on the fuzzy set theory, formulated and developed by Zadeh [1]. Fuzzy set theory is a generalization of classical set theory that provides a way to absorb the uncertainty inherent to phenomena whose information is vague and supplies a strict mathematical framework, which allows its study with some precision and accuracy. A fuzzy logic system (FLS) can deal with the vagueness and uncertainty residing in the knowledge possessed by human beings or implicated in the numerical data, and it allows us to represent the system parameters with linguistic terms[2]. Since the introduction of the basic conceptions of the fuzzy set theory, FLS have been studied for more than 30 years. The success of their applications is in various fields. They can be very helpful to achieve classification tasks, offline process simulation and diagnosis, decision support tools, and process control [3]. Fuzzy rules and membership functions have been used as a key tool to express knowledge. There are (at least) four sources of uncertainties associated with fuzzy logic systems (FLSs) which can be listed as follows:

1- The meanings of the words that are used in the antecedents and consequents of rules can be uncertain (words mean different things to different people). 2-Consequents rnay have a histogram of values associated with them, especially when knowledge is extracted from a group of experts who do not all agree. 3-Measurements that activate a FLS may be noisy and therefore uncertain. 4-The data that are used to tune the parameters of a FLS may also be noisy. All of’ these uncertainties translate into uncertainties about fuzzy set membership functions. Traditional type-I fuzzy sets are not able to directly model such uncertainties because their membership functions are totally crisp. On the other hand, type-2 fuzzy sets are able to model such uncertainties because their membership functions are themselves fuzzy.

Figure.1-Structure of a Type-2 FLS




، دانشگاه فردوسي مشهد ، دانشگاه فردوسي مشهد13861386 شهريور شهريور 77--99 ، ، فازيفازيتمين كنفرانس سيستمهاي تمين كنفرانس سيستمهاي ففهه

Fuzzy Um-set in Sostak senseMohsen Alimohammady and Mehdi Roohi

Department of Mathematics, Faculty of Basic SciencesUniversity of Mazandaran, Babolsar 47416–1468, Iran,

[email protected], [email protected]

Abstract. This paper is devoted to extending the notion of fuzzy minimal space in Sostak sense.The concepts of fuzzy Um-set, (U,m)-open set and (U,m)-closed set will be introduced and some char-acterizations of them are achieved. Finally, some brand of fuzzy minimal continuous functions and theirrelations with fuzzy Um-set, (U,m)-open set and (U,m)-closed set are given.

1 Introduction

After the discovery of the fuzzy sets, many at-tempts have been made to extend various branchesof mathematics to the fuzzy setting. Fuzzy topo-logical spaces as a very natural generalization oftopological spaces were first put forward in the lit-erature by Chang [11] in 1968. He studied a numberof the basic concepts including interior and closureof a fuzzy set, fuzzy continuous mapping and fuzzycompactness. Several authors used Chang’s defini-tion in many direction to obtain some results whichare compatible with results in general topology.In 1976 Lowen [17] suggested an alternative andmore natural definition for achieving more resultswhich are compatible to the general case in topol-ogy. For example with Chang’s definition, constantfunctions between fuzzy topological spaces are notnecessarily fuzzy continuous but in Lowen’s senseall of the constant functions are fuzzy continuous.In 1985 Sostak [25] introduced the smooth fuzzytopology as an extension of Chang’s fuzzy topol-ogy. It has been developed in many directions [12],[14] and [15].

In [20] authors introduced minimal structuresand minimal spaces. Some result about minimalspaces can be found in [2], [7], [13], [18], [19], [22]and [24]. The concept of fuzzy minimal structurewas introduced and studied in [1], [3], [4], [5], [6]and [8] which it extended fuzzy topology definedby Lowen [17]. In this paper we redefine fuzzyminimal structure as a function which is a general-ization of fuzzy topology introduced by Sostak [25].

2 Preliminaries

For easy understanding of the material incorpo-rated in this paper we recall some basic definitionsand results. For details on the following notionswe refer to [23], [25] and [26]. A fuzzy set in(on)a universe set X is a function with domain X andvalues in I = [0, 1]. The class of all fuzzy sets onX will be denoted by IX and symbols A,B,... isused for fuzzy sets on X. 01X is called empty fuzzy

set where 1X is the characteristic function on X. Afamily τ of fuzzy sets in X is called a fuzzy topologyfor X if

(a) α1X ∈ τ for each α ∈ I,

(b) A ∧B ∈ τ , where A, B ∈ τ and

(c)W

α∈AAα ∈ τ whenever, Aα ∈ τ for all αin A. The pair (X, τ) is called a fuzzy topologicalspace [17]. Every member of τ is called fuzzy openset and its complement is called fuzzy closed sets[17]. In a fuzzy topological space X the interior andthe closure of a fuzzy set A (denoted by Int(A) andCl(A) respectively) are defined by

Int(A) =_{U : U ≤ A, U is fuzzy open set} and

Cl(A) =^{F : A ≤ F, F is fuzzy closed set}.

Let f be a function from X to Y . It is a fuzzyfunction defined by

f(A)(y) =

8<:W

x∈f−1({y})A(x) f−1({y}) 6= ∅

0 f−1({y}) = ∅,

for all y in Y , where A is an arbitrary fuzzy set inX [27].

Definition 2.1. Let (X, τ) be a fuzzy topologicalspace. A fuzzy set A in X is said to be

(a) fuzzy semi open if A ≤ Cl(Int(A)) [9],

(b) fuzzy preopen if A ≤ Int(Cl(A)) [10],

(c) fuzzy α-open if A ≤ Int(Cl(Int(A))) [10],

(d) fuzzy β-open if A ≤ Cl(Int(Cl(A))) [21].

The family of all fuzzy semi open, fuzzy pre-open, fuzzy α-open and fuzzy β-open sets isdenoted by FSO(X), FPO(X), FαO(X) andFβO(X) respectively. The complement of a fuzzysemi open, fuzzy preopen, fuzzy α-open and fuzzyβ-open set is called fuzzy semi closed, fuzzy pre-closed, fuzzy α-closed and fuzzy β-closed respec-tively. The union of all fuzzy semi open, fuzzy pre-open, fuzzy α-open and fuzzy β-open sets of X con-tained in A is called fuzzy semi interior, fuzzy prein-terior, fuzzy α-interior and fuzzy β-interior of Aand is denoted by sInt(A), pInt(A), αInt(A) and

1



29-31 Aug 2007

71

xN

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Velocity Control of an Electro Hydraulic Servosystem by Sliding Mamdani

Abstract- This paper addresses new hybrid approaches for velocity control of an electro hydraulic servosystem

(EHSS) in presence of flow nonlinearities and internal friction. In our new approaches, we combined classical method based-on sliding mode control and Mamdani networks. The control by using adaptive networks need plant’s Jacobean, but here this problem solved by sliding surface. It is demonstrated that this new technique have good ability control performance. It is shown that this technique can be successfully used to stabilize any chosen operating point of the system. All derived results are validated by computer simulation of a nonlinear mathematical model of the system. The controllers which introduced have big range for control the system.

Keywords: Electro Hydraulic, Mamdani networks, Strict Feedback, Sliding mode, Sliding Surface.

1 Introduction The EHSS is used in many industrial applications, because of its ability to handle large inertia and torque loads and, at the same time, achieve fast responses and a high degree of both accuracy and performance [1, 2].

Depending on the desired control objective, an EHSS can be classified as either a position, velocity or force/torque EHSS. Therefore, control techniques for electro-hydraulic servo system have been widely studied over the past decade; the details of these systems are given in the reference [3]. In [8] an intelligent CMAC neural network controller using feedback error learning approach introduced which is very complex, and [3] presents methods based on feedback linearization and backstepping approaches, that have good performances but the controller designing is not very simple procedure, in [9] authors proposed a simpler method than other methods based on Lyapunov stability approach but the results in this new hybrid approaches are very better and faster than other mentioned methods.

The paper is organized like this: In section 2, the EHSS and its nonlinear mathematical model are described. In section 3, issues related to the sliding mode design and Mamdani network are discussed

in some detail. In section 4, system properties and the relation of new method and simulation results describe and section 5 is the conclusion part.

2 System Description

A scheme of an electrohydraulic velocity servosystem is shown in Figure 1. The basic parts of this system are: 1. hydraulic power supply, 2. accumulator, 3. charge valve, 4. pressure gauge device, 5. filter, 6. two-stage electrohydraulic servovalve, 7. hydraulic motor, 8. measurement device, 9. personal computer, and 10. Voltage- to- current converter.

Figure 1: Electrohydraulic velocity servosystem.

A mathematical representation of the system is derived using Newton’s Second Law for the

M. Aliyari Shoorehdeli1, M. Teshnehlab2

1. Computer department of Science and Research Branch, Islamic Azad University

of Tehran, Iran. 1, 2. K. N. Toosi University of Tech Tehran, Iran.

[email protected], {m_aliyari, teshnehlab}@eetd.kntu.ac.ir



29-31 Aug 2007

103

An On-line Fuzzy Backstepping Controller for Rotary Inverted Pendulum System

Mahsa Rahmanian1, Mahdi Aliyari Shoorehdeli2, Mohammad Teshnehlab3

1, 2 Computer Department, Science & Research Branch, Islamic Azad University

3 Electrical Department, K. N. Toosi University of Tech [email protected], [email protected], [email protected]

Abstract: In this study a new combination of nonlinear backstepping scheme with on-line fuzzy system is presented for the rotary inverted pendulum system to achieve better performance in nonlinear controller. The inverted pendulum, a popular mechatronic application, exists in many different forms. The common thread among these systems is their goal: to balance a link on end using feedback control. The purpose of this study is to design a stabilizing controller that balances the inverted pendulum in the upright position. Keywords: Nonlinear backstepping, Fuzzy approximator, Rotary inverted pendulum. 1 Introduction Inverted pendulum has been widely used in both linear and nonlinear control education with applications to other under actuated mechanical systems, involving nonlinear dynamics, robotics and aerospace vehicles testing [1]. Recently, the pioneering work on fuzzy control via backstepping has been done in [2-4]. In which, a fuzzy system is used to approximate the unknown nonlinear function in each design step, and an adaptive fuzzy controller was developed by meaning of backstepping technique for a class of SISO uncertain nonlinear systems [5]. The rotary motion inverted pendulum, which is shown in Fig (1-a), is driven by a rotary servo motor system [6]. The zero position for α and θ are defined as the pendulum being vertical ‘up’.

This paper introduces a new combination of backstepping scheme with an on-line fuzzy system to obtain a nonlinear controller to stabilize the pendulum at the upright equilibrium point. 2 System Model and Dynamics Here, in this part the description of model and dynamics are given. Fig (1-a) depicts the rotary inverted pendulum in motion. Fig (1-b) depicts the pendulum as a lump mass at half the length of the pendulum. By applying the Euler-Lagrange equations, we can obtain the equations of motion as follows: ( ) ( ) ( ) θααααθ &&&&&&

eq2

eq2 BT mrLCos mrLSin Jmr −=−++

( ) ( ) 0mgLSin mrLCosmL34 2 =−− αθαα &&&&

where L is the length to pendulum's center of mass, m is the mass of pendulum arm, r is the rotating arm length, θ is the servo load gear angle, α is the pendulum arm deflection, eqJ is the equivalent

moment of inertia at the load, eqB is the equivalent viscous damping coefficient, g is the gravitational acceleration and T is the control torque. The Eq.(1) can be rewritten as the following state equations:

42

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xxxx

==

&

&

)1(




Optimal Design of Type_1 TSK Fuzzy Controller Using GRLA

F. Naderi, A. A. Gharaveisi and M. Rashidinejad Electrical Engineering Dept. of Shahid Bahonar University of Kerman

Kerman, Iran [email protected]

ABSTRACT A new methodology for designing optimal systematic GA-based fuzzy controller is presented in this paper. Our design is based on Genetic Reinforcement Learning Algorithm (GRLA), unlike conventional GA that is based on the competition between chromosomes only to survive, this method is based on competition and cooperation between chromosomes, GA tries to find good chromosomes and good combination for them to form an optimal fuzzy controller. The proposed GRLA design method has been applied to the cart-pole balancing system. The controller was capable of balancing the pole for initial conditions up to 80 ° . As a comparison we applied a Mamdani controller which is designed through normal GA and uses five membership functions for inputs and output variables to the same problem. the results show the efficiency of the proposed method. Keywords : Genetic Reinforcement Learning Algorithm (GRLA), TSK Fuzzy Controller

I. INTRODUCTION Fuzzy theory has been developed by L.A.Zadeh in 1965 [1]. Since conventional control schemes are limited in their range of practical applications, fuzzy logic controllers are receiving increased attention for intelligent control applications [2]. Fuzzy control systems employ a mode of approximate reasoning that resembles the decision-making process of humans. The behavior of a fuzzy controller is easily understood by a human expert as knowledge is expressed by means of intuitive, linguistic rules. In the design of a fuzzy controller the definition of membership functions and the establishment of control rules (if-then rules) are very important. In [5], Procyk and Mamdani show that a change in the membership function (mf) may alter the fuzzy control system (FCS) performance significantly. Unfortunately the human experts are not sometimes able to express their knowledge in the form of fuzzy

if-then rules. So this fact has forced researchers to find a method that automatically determines the parameters. Some papers propose automatic methods using neural networks (NN) [7,8] ,Fuzzy clustering [6] ,genetic algorithms(GA) [3,9,10,11,12] , gradient methods[13,14], or Evolutionary Algorithm (EA) [4,22,23]Karr used a GA to generate membership function for a fuzzy controller [15] in Karr’s work , the user has to define a method to set the rules at first or hand-design this exhaustive task, then use the GA to design the mf only. Since the mf and rule set are highly dependent, hand-design a one, and GA-design of the other, does not use the GA to its full advantage. So in most automatic designs For an FCS the optimization of both the Membership function (mf) and the control rules of the FCS are required. Berenji [16, 17] introduced a method that learns to adjust the fuzzy mf of the linguistic labels used in different control rules through




System of linear fuzzy differential equations

Abstract: In this paper, we discuss the solution of a system of linear fuzzy differential equations,

where A and B are real nn× matrix and the initial condition 0x is described by a vector made up of n fuzzy numbers. In this paper, we investigated a necessary and sufficient condition for the existence derivative )(

.tx of a fuzzy process x(t).

Keywords: Fuzzy number, Linear fuzzy differential equations, Fuzzy system

1. Introduction The concept of fuzzy numbers and fuzzy rithmetic operations were first introduced by Zadeh [19], Dubois and Prade[8]. We refer the reader to [9] for more information on fuzzy numbers and fuzzy arithmetic. Fuzzy systems are used to study a variety of problems ranging from fuzzy topological spaces [6] to control chaotic systems [11], fuzzy metric spaces [17], fuzzy differential equations [3], fuzzy linear systems [1,2]. One of the major applications of fuzzy number arithmetic is treating system of linear fuzzy differential equations [20]. In modelling real systems one can be frequently confronted with a differential equation

where the structure of the equation is known, represented by the vector field f, but the model parameters and the initial value 0x are not known

exactly. One method of treating this uncertainty is to use a fuzzy set theory formulation of problem [18]. The topic of Fuzzy Differential Equations (FDEs) has been rapidly growing in recent years. The concept of fuzzy derivative was first introduced by Chang and Zadeh [5] , it was followed up by Dobois and Prade [7] who used the extension principle in their approach. Other ethods have been discussed by Puri and Ralescu [10]. fuzzy differential equations were first formulated by Kaleva [9] and Seikkala [18] in time dependent form. Kaleval had formulated fuzzy differential equations, in term of derivative [9]. Buckley and Feuring \cite{bf} have give a very general formulation of a fuzzy first-order initial value problem. They first find the crisp solution, fuzzify it and then check to see if it satisfies the FDE. Pearson \cite{pear} has a property of linear fuzzy differential equations,

M. Otadi a , S. Abbasbandy b and M. Mosleh a

a Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh, Iran

b Department of Mathematics, Faculty of Science, Imam Khomeini International University, Ghazvin, 34149-16818, Iran

[email protected] , [email protected],

[email protected]



29-31 Aug 2007


A method for

fully fuzzy linear system of equations

H. Rouhparvar ∗, T. Allahviranloo †

∗Department of Mathematics, Saveh Branch, Islamic Azad University, Saveh, Iran†Department of Mathematics, Science and Research Branch,

Islamic Azad University, Tehran, Iran

Abstract :Fuzzy linear systems of equations play amajor role in various applications such as financial,economics, engineering and physics. We employ newproduct-type operation which are introduced and studiedin [4], as e.g. the cross product of fuzzy numbers thatfrom the theoretical and practical point of view in fuzzyarithmetic, is efficiently of the multiplication based onZadeh’s extension principle for finding a fuzzy vector xwhich satisfies Ax = b, where An×n and b are a fuzzymatrix and a fuzzy vector, respectively. We transformfully fuzzy linear system of equations (FFLSEs) toextended crisp linear system in [12]. This systems canbe solve as numerically, see [1, 2, 3, 6].

Keywords: Fully fuzzy linear system of equations,Cross product, Fuzzy number, Fuzzy matrix.

1 Introduction

Fuzzy linear system, Ax = b, where the coefficient ma-trix A is crisp, while b is a fuzzy number vector, issolved in [12, 13, 14]. Friedman et al. [12] use the em-bedding method given in [19]. Allahviranloo [1, 2, 3]uses the iterative Jacobi and Gauss Siedel method, theAdomian method and SOR method, respectively. Ofcourse, the a lot of papers with different methods ex-ist in this content but in continuation to these works,people worked the case in which all parameters in afuzzy linear system are fuzzy numbers, which we callit a Fully Fuzzy Linear System of Equations(FFLSEs),for example see [8, 16, 18].

Here we will solve A⊗ x = b, where A is a fuzzy ma-trix and x and b are fuzzy vectors. We will use fuzzymatrix defined in [10]. This class of fuzzy matrices con-sist of applicable matrices, which can model uncertain

∗Email address: [email protected].

aspects and the works on them are too limited. Someof the most interesting works on these matrices can beseen in [5, 9]. In [8] a computational method repre-sented for solving a FFLSEs based on Zadehs exten-sion principle and in [18] provided a method to solvethis problem based on their cuts. Now we provide amethod based on r-cuts and new definition of productfuzzy numbers, i.e., the cross product to solve FFLSEsis computational and practical. In this paper we usetriangular fuzzy numbers.

The structure of this paper is organized as follows:In Section 2, we recall some concepts from fuzzy arith-metic. We illustrate summary of the cross product inSection 3. In Section 4, we solve A ⊗ x = b by pro-posed method. The proposed method are illustratedby solving some examples in section 5 and conclusionare drawn in Section 6.

2 Preliminaries

In this section we represent definitions needful for nextsections. We denote by E1 the set of all fuzzy numbers.

2.1 Fuzzy numbers

Definition 2.1. A fuzzy subset u of the real line Rwith membership function u(t) : R → [0, 1] is called afuzzy number if:

(a) u is normal, i.e., there exist an element t0 suchthat u(t0) = 1,

(b) u is fuzzy convex, i.e., u(λt1 + (1 − λ)t2) ≥min{u(t1), u(t2)} ∀t1, t2 ∈ R, ∀λ ∈ [0, 1],

(c) u(t) is upper semi continuous,

1



29-31 Aug 2007


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Full fuzzy linear systems of the form Ax+b=Cx+d

Abstract: This paper mainly intends to discuss the solution of the full fuzzy linear systems (FFLS) Ax+b=Cx+d, where A and C are fuzzy matrices, b and d are fuzzy vectors. Ming Ma et al. introduced a new fuzzy arithmetic based on parametric form of fuzzy numbers, which we apply it for our purpose. Keywords: Fuzzy number, Full fuzzy linear systems, Fuzzy arithmetic, Parametric epresentation

1. Introduction The concept of fuzzy numbers and fuzzy arithmetic operations were first introduced by Zadeh [16], Dubois and Prade [7]. Fuzzy systems are used to study a variety of problems ranging from fuzzy topological spaces [5] to control haotic systems [8,11], fuzzy metric spaces [14], fuzzy differential equations [3], fuzzy linear systems [1,2]. One of the major applications of fuzzy number arithmetic is treating fuzzy linear systems and fully fuzzy linear systems, several problems in various areas such as economics, engineering and physics boil down to the solution of a linear system of equations. In many applications, at least some of the parameters of the system should be represented by fuzzy rather than crisp numbers. Thus, it is immensely important to develop numerical procedures that would appropriately treat fuzzy linear systems and solve them. Friedman et al. [9] introduced a general model for solving a fuzzy nn× linear system whose coefficient matrix is crisp and the right-hand side

column is an arbitrary fuzzy number vector. They used the parametric form of fuzzy numbers and replaced the original fuzzy nn× linear system by a crisp nn 22 × linear system and studied duality in fuzzy linear systems Ax=Bx+y where A , B are real nn× matrices, the unknown vector x is vector consisting of n fuzzy numbers and the constant y is vector consisting of n fuzzy numbers, in [10]. In [1,2] the authors presented conjugate gradient, LU decomposition method for solving general fuzzy linear systems or symmetric fuzzy linear systems. Also, Wang et al. [15] presented an iterative algorithm for solving dual linear system of the form x=Ax+u, where A is real nn× matrix, the unknown vector x and the constant u are all vectors consisting of fuzzy numbers and abbasbandy [4] investigated the existence of a minimal solution of general dual fuzzy linear equation system of the form Ax+f=Bx+c, where A, B are real nm× matrices, the unknown vector x is vector consisting of n fuzzy numbers and the onstant f, c are vectors consisting of $m$ fuzzy numbers. Recently, Muzziloi et al. [13] considered fully fuzzy linear systems of the form

M. Mosleh a , S. Abbasbandy b and M. Otadi a a Department of Mathematics, Islamic Azad

University, Firuozkooh Branch, Firuozkooh, Iran b Department of Mathematics, Faculty of Science, Imam Khomeini

International University, Ghazvin, 34149-16818, Iran [email protected], [email protected],

[email protected]



29-31 Aug 2007


Solving fuzzy polynomial equation by ranking method

Abstract: In this paper, we find real roots for fuzzy polynomial equations (if exists) by ranking fuzzy numbers. We transform fuzzy polynomial equation to system of crisp polynomial equations, this transformation perform with ranking method based on three parameters Value, Ambiguity and Fuzziness. Provided system of crisp polynomial equations can be solved numerically. Finally, we illustrate our approach by numerical examples. Keywords: Fuzzy number, Fuzzy polynomial, Value, Ambiguity, Fuzziness. 1 Introduction Polynomial equations play a major role in various areas such as mathematics, engineering and social sciences. We interested in finding real roots of polynomial equation like

, that ℜ∈x (if exists) and nCCC ,,, 10 K are fuzzy numbers, by a ranking method of fuzzy numbers. This ranking method is provided for canonical representation of the solution of fuzzy linear system in [10]. The applications of fuzzy polynomial equations are considered by [2]. Also, numerical solution of fuzzy polynomial equations by fuzzy neural network is solved in [3] and linear and nonlinear fuzzy equations are shown by [1,4,5,6]. In this paper, we propose a new method for solving an fuzzy polynomial equation based on ranking method which is introduced by Delgado et. al. [7,8]. They introduced three real indices called Value, Ambiguity and Fuzziness to obtain "simple", fuzzy numbers, that could be used to represent more arbitrary fuzzy numbers. Therefore, we use this parameters and transform fuzzy polynomial equation to system of crisp polynomial equations then with solving this system we can find real roots of fuzzy polynomial equation.

In Section 2, we review basic definition and the notions of fuzzy numbers, Value, Ambiguity and Fuzziness. In Section 3, we represent fuzzy polynomial equation and proposed method for solving it and provide two total examples. Some numerical examples are considered in Section 4 and Conclusion comes in Section 5. 2 Preliminaries In this section, we review some preliminaries which are needed in the next section. For more details, see [7,8,9]. Definition 2.1. A fuzzy subset C of the real line ℜ with membership function ]1,0[:)( →ℜxC is called a fuzzy number if

1. C is normal, i.e., there exist an element 0x such that 1)( 0 =xC ,

2. C is fuzzy convex, i.e., ))1(( 21 xxC λλ −+ { } ]1,0[,,)(),(min 2121 ∈∀ℜ∈∀≥ λxxxCxC ,

3. )(xC is upper semi continuous, 4. support C is bounded, where

support { }0)(: >ℜ∈= xCxclC ,and cl is the closure operator.

H. Rouhparvar Department of Mathematics, Saveh Branch, Islamic Azad University, Saveh, Iran

[email protected]



29-31 Aug 2007


Stabilization of Autonomous Bicycle by an Intelligent Controller

N. Noroozi and F. Shabani Nia

Department of Electrical Engineering, Shiraz University, Shiraz, Iran

Abstract: Nowadays, urban traffic jams cause waste of time and air pollution. Bicycle is a convenient alternative as a mean of transportation for being confronted with these problems. However, bicycle is unstable in itself and it will fall down without human assistance like steering handle or moving upper body. It needs practice to ride a bicycle [1]. In this paper, an intelligent controller is proposed, which can stabilize a bicycle with suitable performance for the whole of considered range of disturbance. The original part of controller is consists mainly of a fuzzy controller. Also it is used genetic algorithms and neural networks for optimization and adaptation of scaling factors respectively. Keywords: Bicycle, Fuzzy Controller, Stability, Genetic Algorithms, Neural Networks I. Introduction

Nowadays, urban traffic jams cause waste of time and air pollution. Bicycle will help to solve these problems. In addition, the energy conversion efficiency of bicycle is critically higher than other vehicles [2]. Soft computing approaches in decision making have become increasingly popular in many disciplines. This evident from the vast number of technical papers appearing in journals and conference proceeding in all areas of engineering, manufacturing, sciences, medicine, and business. Soft computing is a rapidly evolving field that combines knowledge, techniques from neural networks, fuzzy set theory, and approximate reasoning, and using optimization methods such as genetic algorithms. The integration of these and other methodologies forms the core of soft computing [6].

This paper presents an intelligent controller for stabilization of bicycle by controlling its steering. The original part of controller is consists mainly of a fuzzy controller. Also it is used

genetic algorithms for optimization of response. Neural networks are proposed the controller to conform. This paper is composed of five sections. In section II, dynamic modeling is shown. Section III shows the proposed control strategy. In section IV simulation results are implemented to verify the proposed control strategy. The conclusions are summarized in section V.

II. The Model Assuming that the rider doesn't move upper body, the dynamic model of bicycle is represented as follows [1]

h .F TI CF GR +=θ&& ( 1 ) where I, TGR, FCF, h, and θ mean moment of inertia, gravitational force, centrifugal force, height of COG, and camber angle of bicycle respectively as shown Fig.1.



29-31 Aug 2007



Solving fuzzy linear programming problems with piecewise linear

membership functions by the determination of a crisp maximizing decision

Abstract: In this paper, we concentrate on linear programming problems in which both the right-hand side and the technological coefficients are fuzzy numbers.We consider here only the case of fuzzy numbers with linear membership function. The determination of a crisp maximizing decision [2] is used for a defuzzification of these problems. The crisp problems obtained after the defuzzification are non-linear and non-convex in general. We propose here the ”augmented lagrangian penalty function method” and use it for solving these problems. We also compare the new proposed method with well known ”fuzzy decisive set method”. Finally, we give illustrative example and this solve by the new proposed method and compare the numerical solution with the solution obtained from fuzzy decisive set method. Keywords: Fuzzy linear programming, fuzzy number, augmented lagrangian penalty function method, fuzzy decisive set method. 1 Introduction A model in which the objective function is crisp–that is, has to be maximized or minimized– and in which the constraints are or partially fuzzy is no longer symmetrical. Fuzzy linear programming problem with fuzzy coefficients was formulated by Negoita [3] and called robust programming. Dubois and Prade [4] investigated linear fuzzy constraints. Tanaka and Asai [5] also proposed a formulation of fuzzy linear programming with fuzzy constraints and gave a method for its solution which bases on inequality relation between fuzzy numbers. We consider linear programming problems in which both technological coefficients and right-hand-side numbers are fuzzy numbers. Each problem is first converted into an equivalent crisp problem. This is a problem of finding a point which satisfies the constraints and the goal with the maximum degree. The crisp problems, obtained by such a manner, can be non-linear (even non-convex), where the non-linearity arises in

constraints. For solving these problems we use and compare two methods. One of them called the fuzzy decisive set method, as introduced by Sakawa and Yana [7]. In this methoda combination with the bisection method and phase one of the simplex method of linear programming is used to obtained a feasible solution. The second method we use, is the ”augmented lagrangian penalty method”. In this method a combines the algorithmic aspects of both Lagrangian duality methods and penalty function methods. For this kind of problems we consider, this method is applied to solve concrete examples. The paper is outlined as follows. In section 2, we study the linear programming problem in which both technological coefficients and right-hand-side are fuzzy numbers. The general principles of the augmented lagrangian penalty method is presented in section 3. In section 4, we examine the application of this method and fuzzy decisive set method to concrete example.

S. Effati and H. Abbasiyan e-mail:[email protected]

e-mail:[email protected]



29-31 Aug 2007

205

Fuzzy Convex Subalgebras of Residuated Lattice

Shokoofeh Ghorbani and Abbas Hasankhani Department of Mathematics

Shahid Bahonar University of Kerman Kerman, Iran


Abstract: In this paper we define the concept of fuzzy congruence relations, fuzzy subalgebras, fuzzy convex subalgebras on a residuated lattice and we obtain some related results. In particular, we show that there is a one to one corresponding between the set of all fuzzy convex subalgebras and the set of all fuzzy congruence relations in the residuated lattice. Keywords: Residuated lattice, Congruence relation, Convex subalgebra, Fuzzy set, Fuzzy relation. 1 Introduction The concept of residuated lattice was introduced and studied by Krull [7], Dilworth [4], Ward and Dilworth [11], Ward [10], Bables and Dwinger [1] and Pavelka [8]. The origins of residuated theory lie in the study of ideal lattices of rings. Zadeh in [12] introduced the notion of fuzzy set μ in a nonempty set X , as a function from X into

].1,0[ In the next section we review the basic

definitions and some theorems from [2], [3], [5], [9] and [12]. In section 3 we introduce the concept of fuzzy congruence relations on a residuated lattice and we see that the set of all fuzzy congruence relations on a residuated lattice is a complete lattice. In section 4, we define the concept of fuzzy subalgebras; fuzzy convex subalgebras and we obtain some related results. Finally, we show that there is a bijection between the set of all fuzzy convex subalgebras and the set of all fuzzy congruence relations on a residuated lattice. Hence the set of all fuzzy convex subalgebras of residuated lattice is a complete lattice.

2 Preliminaries Definition 2.1[2, 9] A residuated lattice is an algebra )1,0,,,,,( →∗∨∧L where LR1) )1,0,,,( ∨∧L is a bounded lattice, LR2) )1,,( ∗L is a commutative monoid, LR3) bac →≤ if and only if bac ≤∗ for all

Lcba ∈,, .

Theorem 2.2 [6, 8, 9] Let )1,0,,,,,( →∗∨∧L be a residuated lattice. Then we have the following: 1 xx =→1 , 1=→ xx , 11 =→x , 2 yxyx ∧≤∗ , 3 yx ≤ if and only if 1=→ yx , 4 yxyxx ,)( ≤→∗ , 5 zyzxyx ∗→∗≤→ , 6 yx ≤ if and only if zyzx ∗≤∗ , 7 )()( yzxzyx →→→≤→ , 8 )()( zxzyyx →→→≤→ , 9 zyxzyx →∗=→→ )( , 10 zxyxzyx ∗∨∗=∨∗ )( , for all Lzyx ∈,, .



29-31 Aug 2007



Algebraic Fuzzy Subsets of Non-commutative Join Spaces

H. Hedayatia, R. Amerib

a Department of Basic Sciences, Babol University of Technology, Babol, Iranb Department of Mathematics, Faculty of Basic Sciences, University of Mazandaran, Babolsar, Iran

Email: {h.hedayati, ameri}@umz.ac.ir

Abstract

The aim of this note is the study of important alge-braic fuzzy subsets of transposition hypergroups (non-commutative join spaces). In this regards, we first intro-duce the notions of fuzzy closed, fuzzy normal, fuzzyreflexive and fuzzy invertible subsets of transpositionhypergroups and, then we investigate their basic prop-erties.

Keywords: Fuzzy Hypergroup, Fuzzy Closed set,Fuzzy Normal, Fuzzy Invertible, Fuzzy Reflexive.

1 Introduction

The notion of hypergroup introduced by F. Marty [24].Since then many researchers have studied this field anddeveloped it, for example see [2, 4, 8, 9, 10, 11, 12, 19,26]. Transposition hypergroupsare large class of multivalued systems. Many well-known hypergroups such ashypergroups, weak cogroups, join spaces, polygroups,canonical hypergroups, as well as ordinary groups areall transposition hypergroups [19].

The notion of a fuzzy subset introduced by L. Zadehin 1965 [27] as a function from a nonempty setX to unitreal intervalI = [0,1]. Rosenfeld defined the concept ofa fuzzy subgroup of a given groupG [25] and then manyresearchers has developed it in all subject of algebra.

Also fuzzy sets has been a good developed in hyper-alebraic structures theory(for example see [1],[3],[4],[5], [6], [7], [13], [14], [15], [16], [17], [21], [22],[23],[29]).

The second author in [1] introduced some basic re-sults of fuzzy transposition hypergroups. Now in thisnote we follow [1] and introduce some another impor-tant fuzzy subsets of transposition hypergroups, suchas fuzzy normal, fuzzy reflexive and fuzzy invertiblesubsets and then we obtain some related basic resultsof these notions. In section 2 we gather all the pre-

liminaries of hypergroups and fuzzy sets which will beused in the next sections. In section 3 we study fuzzyclosed and fuzzy normal subhypergroups. In section 4we introduce the notions of fuzzy invertible and fuzzyreflexive subset of a hypergroup, and then we investi-gate the relationships between fuzzy closed, fuzzy nor-mal, fuzzy invertible and fuzzy reflexive subsets.

2 Preliminaries

In this section we gather all definitions and simple prop-erties we require of hypergroups and fuzzy subsets andset the notions.

Let H be a nonempty set andP∗(H) the family of allnonempty subsets ofH.

A map . : H×H −→ P∗(H) is calledhyperoperationor join operation.

The join operation is extended to subsets ofH in nat-ural way , so thatA.B or AB is given by

AB=⋃{ab|a∈ A and b∈ B }.

The relational notationA≈ B (readA meetsB) is usedto asserts thatA andB have an element in common, thatis, A∩B 6= /0. The notationsaA and Aa are used for{a}A andA{a} respectively. Generally, the singleton{a} is identified by its elementa.

In H right extension/ and left extension\ are definedby

a/b = { x∈ H | a∈ xb},

b\a = { x∈ H | a∈ bx}.

A hypergroupis a structure(H, .) that satisfies twoaxioms,

(Reproductivity) aH = H = Ha for all a∈ H;(Associativity) a(bc) = (ab)c for all a,b,c∈ H.

1



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An Ant Based Algorithm Approach to Vehicle Navigation

Hojjat Salehi-nezhad and Fereydoun Farrahi-Moghaddam Department of Electrical Engineering,

S.B University of Kerman, Kerman, Iran

[email protected] ffarrahi @mail.uk.ac.ir

Abstract This paper presents an algorithm to search for the best direction between two desired origin and destination intersections in cities using ant algorithms, which is known as Ant-based Vehicle Navigation (AVN) algorithm. As travelers have their own parameters to select a direction, adjustable parameters were considered in this algorithm in order to satisfy the most important passengers’ needs. A practical model of this algorithm has applied on a part of Kerman city and its validity was examined. By using this AVN algorithm the traffic problem could be decreased efficiently without employing geographical positioning system (GPS). Keywords: Ant algorithms; Vehicle navigation; Vehicle traffic; Travel time 1. Introduction ACO algorithm has plenty of applications in network problems such as water distribution networks [18], computer networks [7] and transportation networks [17]. For example, in computer network problems, routing of packets and finding paths from source to destination nodes has a closed relation with the cost and type of utilization of that network. ACO with its specific type of agents is a perfect tool for optimization of such networks, which results in reducing cost in path finding and packet routing [7]. Transportation networks are similar to computer networks by considering vehicles as network packets and routes as network connections, therefore same solution could be used for both types of networks. In this paper an algorithm is proposed to find the best direction satisfying city travelers using ant algorithms. Although real ants are blind, they are capable of finding the shortest path from food source to their nest by exploiting information of a liquid substance called pheromone, which they

release on the route transiting in. By means of this, they do their complex daily activities such as finding and sorting foods. The idea of employing the foraging behavior of ants as a method of stochastic combinatorial optimization was initially introduced by Dorigo in his PhD thesis [1]. This is very important for travelers to get the best direction relevant to their preferences, even though they be familiar or unfamiliar with a city. We want to use ants for finding the best path between two specific locations according to different local and statistical parameters important for city travelers supporting them. This paper is organized as follows. The next section and section 3 reviews the basic principles of the ACS algorithm and AVN algorithm respectively. Sections 4 renders the details of the proposed method and experimental results are presented in section 5. Finally, the paper in concluded in section 6.



29-31 Aug 2007


Novel ranking method of fuzzy numbers

Abstract: In this paper, a novel method for ranking of fuzzy numbers is proposed. This method is based on the center of mass at some α-cuts of a fuzzy number. Our method can rank more than two fuzzy numbers simultaneously. Also some properties of method are described. At last, we present some numerical examples to illustrate our proposed method, and compare them with other ranking methods.

Keywords: Ranking fuzzy numbers; Center of mass.

1 Introduction For ranking of fuzzy numbers, a fuzzy number needs to be evaluated and compared with the others, but this may not be easy. Since fuzzy numbers are represented by possibility distributions, they can overlap with each other and it is difficult to determine clearly whether one fuzzy number is larger or smaller than another. Fuzzy set ranking has been studied by many researchers. Some of these ranking methods have been compared and reviewed by Bortolan and Degain [2]. More recently by Chen and Hwang [3], and it still receives much attention in recent years [5, 10, 17, 18]. Many methods for ranking Fuzzy numbers have been proposed, such as representing them with real numbers or using fuzzy relations. Wang and Kerre [18, 12] proposed some axioms as reasonable properties to determine the rationality of a fuzzy ranking method and systematically compared a wide array of existing fuzzy ranking methods. Almost each method, however, has pitfalls in some aspect, such as inconsistency with

human intuition, indiscrimination, and difficulty of interpretation. What seems to be clear is that there exists no uniquely best method for comparing fuzzy numbers, and different methods may satisfy different desirable criteria. In the existing fuzzy number ranking methods, many of them are based on the area measurement with the integral value about the membership function of fuzzy numbers [5, 20, 17, 21, 7, 11, 13, 9, 14, 18, 16, 15]. Yager [8] proposed centroid index ranking method with weighting function. Cheng [4] proposed a centroid index ranking method that calculates the distance of the centroid point of each fuzzy number and original point to improve the ranking method [23]. They also proposed a coefficient of variation (CV index) to improve Lee and Lis method [16]. Recently, Tsu and Tsao [6] pointed out the inconsistent and counter intuition of these two indices and proposed ranking fuzzy numbers with the area between the centriod point and original point. The rest of our work is organized as follows. Section 2, contains the basic definitions and notations used in the remaining parts of the paper. In Section 3, introduces the ranking method and

M. Barkhordary a T. Allahviranloo b T. Hajjaric

a Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran b Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran, 14515, Iran

c Department of Mathematics, Firuz Kuh Branch, Islamic Azad University, Firuz Kuh, 132, Iran [email protected],




29-31 Aug 2007



A Trapezoidal Membership Function Block for Fuzzy Applications

Abstract: A new Switched Capacitor Membership Function circuit, which is based on an offset insensitive SC amplifier and presenting trapezoidal-shape transcharacteristics is proposed. The circuit is realized in a 0.35-um standard CMOS technology and simulation by Hspice is carried out. Keywords: Fuzzy rule, Membership degree, Memebership Function Block, Trapezoidal MFB.

1 Introduction

Over recent years, due to inherent ability of fuzzy signal processing in expressing complex control laws by using simple systems of rules, application of fuzzy systems has become very popular [2-3]. Moreover, in some applications, fuzzy control has been proved to achieve better performances with respect to conventional methods. A large number of basic building blocks [5-8] or fuzzy systems, suitable for a VLSI digital or analog implementation, are contained in literature. In particular, digital implementations have the advantage of both simple design procedure and good accuracy but they require a larger silicon area with respect to equivalent analog ones. This area occupation increases if the circuit has to communicate with the real world because A/D and D/A converters are mandatory for both inputs and outputs. On the other hand, analog implementation has better performances in terms of silicon area and speed requirements, but they need a large effort during the design. The Switched Capacitor (SC) technique appears to constitute a good compromise between speed, accuracy, area and effort of design. In fact, although its speed limitation compared to a continuous-time implementation, it provides the benefits of both small area occupation and good accuracy. Moreover, the efforts during the circuit realization can be minimized by using macro cells of fundamental blocks (opamps, switches,

capacitive arrays, etc.), thus simplifying the layout process. A fundamental cell in fuzzy systems is the Membership Function Block (MFB) which returns the membership degree of a variable with respect to a given fuzzy set. In this paper, modifying a triangular-shape Membership Function Block, a trapezoidal-shape Membership Function Block in SC technique is presented. The proposed MFB is realized in a 0.35um standard CMOS technology and simulation results are given.

2 The Transcharacteristic equation

A trapezoidal MFB, shown in fig.1 can be mathematically represented by the following equations:

max1

max1 max 1 1

max 1 2

max2 max 2 2

max2

0

( )

( )

0

in t

in t t in t

out t in t

in t t in t

in t

VV V

VV V V V V V

V V V V VVV V V V V V

VV V

α

αα

αα

α

⎧ ⟨ −⎪⎪⎪ − + − ⟨ ⟨⎪⎪= ⟨ ⟨⎨⎪⎪− − + ⟨ ⟨ +⎪⎪

⟩ +⎪⎩

(1)

Referring fig. 1 parameters a and Vmax represent the slope of the transcharacteristic and its maximum value respectively, while Vt1 and Vt2 show the interval during which the trapezoid reaches its maximum value.

S. Momeni, A. Khoei*, Kh. Hadidi and Gh. Yosefi+ Department of Microelectronic laboratory of Urmia University, Urmia 57159, Iran

* [email protected] + [email protected]



29-31 Aug 2007

293

Ranking Fuzzy Numbers by Sign Length

T. Hajjari, M. Barkhordary

Department of Mathematics, Firuz Kuh Branch, Islamic Azad University, Firuz Kuh, 132, Iran Department of Mathematics, Bandar Abbas Branch, Islamic Azad University, Bandar Abbas, Iran

[email protected], mahnaz [email protected]

Abstract : Several strategies have been proposed for ranking of fuzzy numbers. Each of these techniques has been shown to produce non-intuitive results in certain cases. In this paper,we introduce an approximate method for ranking of fuzzy numbers based on the centroid point of the surface bounded above by the graph of the membership function of fuzzy number below by X-axis. The calculation of proposed method is far simple than the other approaches. Keywords: Ranking, Fuzzy Numbers, Centroid Point. 1 Introduction In many applications, ranking of fuzzy numbers is an important component of the decision process. Many authors have investigated the use of fuzzy sets in ranking alternatives and they have studied different methods of raking fuzzy sets. Particularly, the ranking of fuzzy numbers. In 1976 and 1977, Jain [17, 18] proposed a method using the concept of maximizing set to order the fuzzy numbers. Jain’s method is that the decider considers only the right side membership function. A canonical way to extend the natural ordering of real numbers to fuzzy numbers was suggested by Bass and Kwakernaak [8] as early as 1977. Dubios and Prade 1978 [15], who used maximizing sets to order fuzzy numbers. In 1979, Baldwin and Guild [5] indicated that these two methods have some disturbing disadvantages. Also in 1980, Adamo [3] used the concept of -level set in order to introduce _-preference rule. In 1981 Chang [6] introduced the concept of the preference function P(A) of an alternative A. Yager in 1981 [25, 26] proposed four indices which may be employed for the purpose of ordering fuzzy quantities in [0, 1]. Bortolan and Degani [7], Chen [9], Choobineh [11], Cheng [10] have presented some methods , and also more recently some numerous ranking techniques have been purposed and investigated by Chu, Tsao [12] and

Ma, Kandel and Friedman [21]. Nowadays many researchers have developed methods to compare and to rank fuzzy numbers. Some of those methods are counter-intuitive and non discriminating [1, 2, 7, 13, 22, 24]. Thus it causes a natural need of defuzzification of a fuzzy numbers which is easy to handle and have a natural interpretation. In [1] is defined a metric between fuzzy numbers. Then it used to rank the fuzzy numbers and it is called ranking by sign distance. Furthermore, it is compared with some previous methods. Asady and Zendehdel also give a new method in [4] which is called ”distance minimization”. Now we turn to introduce our proposed approach. In this paper the idea of the ordering of fuzzy quantities are to convert a fuzzy quantity into a real number and base the comparison of fuzzy quantities on that of real numbers. In the other words, our method is placed in the first class of Kerre’s categories [23]. The rest of paper is organized as follows. Section 2 contains the basic definitions and notations use in the remaining parts of the paper. In Section 3, we will introduce our idea and investigate some properties of our method. Some numerical examples are illustrated and are compared with some previous methods in Section 4. The final section is conclusion.




29-31 Aug 2007

297

Ranking of fuzzy numbers by left and right ranking Functions

B. Agheli , M. Adabitabar Firozja

Department of mathematics, Islamic Azad University, Qaemshahr, Iran [email protected]

Abstract: In this paper we proposed a new approach for ranking of fuzzy numbers with membershipfunction. Initially the membership function of comparison between crisp and fuzzy numbers is proposed. We extend it to ranking of fuzzy numbers. Finally we compare the proposed definitionwith some of the known ones. Keywords: Fuzzy Numbers; Ranking. 1 Introduction Recently, fuzzy systems are used to study a variety of problems ranging from fuzzy topological spaces to control chaotic systems, fuzzy metric spaces,fuzzy linear systems and particle physics. The concept of fuzzy numbers and arithmetic operations with this numbers were first introduced and investigated by Zadeh and others. Fuzzy ranking is a topic which has been studied by many researchers, too[1,7,4,6,8]. Each method has a shortcoming. But, in this study the membership function of ranking between crisp and fuzzy numbers is proposed and then it is used for ranking fuzzy numbers. The paper is organized as follows: Background on fuzzy concepts is presented in section 2. A com-parison between crisp and fuzzy numbers with its properties is introduced in section 3. Subsequently, in section 4 a ranking between two fuzzy numbers with its properties for fuzzy numbers is considered. Then in section 5, for comparing of new approach with some of other approaches some numerical examples are brought. Finally, conclusion is drawn in Section 6. 2 Background A fuzzy set is a generalized left right fuzzy numbers (GLRFN) of Dubois and Prade [5, 7], if its membership function satisfy the following:

(1)

Where L and R are strictly decreasing functions defined on [0, 1] and satisfying the conditions: (2)

A GLRFN is denoted as and an α-level interval of fuzzy number as:

(3)

3 Comparison between crisp and fuzzy number Let and x be a crisp number then we define the degree of omparison fuzzy number A˜ and crisp number x as follows:

),,,(~4321 aaaaA =

⎪⎪⎪

⎩

⎪⎪⎪

⎨

⎧

≤≤−−

≤≤

≤≤−−

=

otherwise

axaaaaxR

axa

axaaaxaL

xA

,0

),(

,1

),(

)(

4334

3

32

2112

2

~μ

10)()(01)()(

≥==≤==

tiftRtLtiftRtL

LRaaaaA ),,,(~4321=

A~

)]()(),()([

)](),([][1

3431

122 αα

ααα

−− −+−−=

=

RaaaLaaa

AAA rl

GLRFNaaaaA ∈= ),,,(~4321

A~



29-31 Aug 2007



An Application of Possibility Goal Programming to the Time-Cost Trade off Problem

M.Ghazanfari1, K.Shahanaghi2, A.Yousefli3

Department of Industrial Engineering, Iran University of Science and Technology, Tehran, Iran 1:[email protected] 2:[email protected] 3:[email protected]

Abstract: Activity duration is uncertain due to the variations in the real world such as weather, resource availability, etc. Utilization of uncertain planning leads to project scheduling with more stability against environmental variations. This paper presents a new optimal model for time-cost trade-off problem in fuzzy environment. In order to solve this problem, we develop a new possibility goal programming approach. Significant feature of this model is determination of optimal activity duration in form of triangular fuzzy numbers. To validate the algorithm developed here, a case study will be presented.

Keywords: time-cost trade off, possibility goal programming, fuzzy sets, fuzzy decision variable. 1 Introduction Since the late 1950s, Critical-Path-Method (CPM) techniques have become widely recognized as valuable tools for the planning and scheduling of projects. But in many cases, project should implement before the date that was calculated by CPM method. Achieving this goal, can be used more productive equipment or hiring more workers. But it is clear that the project cost increase. Therefore we should find the most cost effective way to complete a project within a specific completion time. Several mathematical and heuristic models have been generated to solve time-cost trade off problems [1]. These models mainly focused on deterministic situations. However, during project implementation, many uncertain variables dynamically affect activity duration, and the costs could also change accordingly. In this paper, we propose an optimal mathematical model to handle the time-cost trade off problems in uncertain environment and a new approach to solve proposed algorithm. 1.1 Literature review of time-cost trade off problem Based upon whether activity duration is certain or not, time-cost trade off models can be categorized into two parts: deterministic scheduling and nondeterministic scheduling. Traditional time-cost trade off models mostly focuses on deterministic situations. Most of these models are heuristic and

analytical. Among them are Siemens's model [2] and Moselhi's model [3]. Some researchers used of operation research's methods to model and solve time-cost trade off problems [4, 5, 6]. Also some methods were developed based on metaheuristic models such as simulated annealing and genetic algorithm [7, 8]. The above-mentioned time-cost trade off models mainly focuses on deterministic situations. Recently, project managers have paid special attention to uncertain scheduling. These models are categorized into two parts: probabilistic models and fuzzy models. Among of probabilistic models is Ang's model [9]. In many projects, required information for estimation of project parameters is not available or is incomplete. Also in many cases the project is under performance for the first time, this compels us to use expert opinion in forecasting the project parameters. Some authors have claimed that fuzzy set theory is more appropriate to model these problems, for example leu et al [1], Hapk and Slowinski [10], Leu et al [11], Wan [12]. 1.2 Literature review of mathematical programming with fuzzy variable Generally speaking, in fuzzy linear programming problems, the coefficients of decision variables are fuzzy numbers whereas decision variables are crisp ones. This means that in an uncertain



29-31 Aug 2007

307

A Multi Hybrid Genetic Algorithm forthe Quadratic Assignment Problem

Abstract: Quadratic assignment problem (QAP) is one of the hardest combinatorial optimization problems which can model many real life problems. Because of its theoretical and practical importance, QAP has attracted attention of many researchers. In this paper, a multi hybrid genetic algorithm for solving QAP is proposed. The key feature of our approach is the hybridization of three metaheuristics, tabu search, simulated annealing and ant system with genetic algorithm. These metaheuristics are used to create a good initial population and later to improve individuals in future generations. Our proposed approach is applied to a number of standard test problems and our computational results are compared with those of three metaheuristics when applied on the same problems alone. It is understood that our approach is one of best algorithms which deals with QAP.

Keywords: Quadratic Assignment Problem, Genetic Algorithm, Tabu Search, Simulated Annealing, Ant System.

1 Introduction

The quadratic assignment problem is a famous combinatorial optimization. Koopmans and Beckmann initially stated this problem in 1957 [20]. The QAP is formulated as follows. Let two matrices nnijfF ][ , nnkldD ][ and the set of the integers from 1 to n be given. Find a permutation

n,...,2,1 that minimizes n

i

n

jjiij dfz

1 1

.

Some of the applications of QAP are described below: campus and hospital planning [5, 10], backboard wiring [28], scheduling [14], design of control panels and typewriter keyboards [26], ranking of archeological data [21], statistical analysis [18], analysis of reaction chemistry [12], numerical analysis [1], placement of electronic components [23] and memory layout optimization in signal processors [32 ]. Sahni and Gonzalez showed that the QAP is NP-hard and that there is no f-approximation polynomial algorithm for the QAP unless P = NP[27]. In general, exact algorithms cannot solve problem instances of size 30n in a reasonable

amount of time. Therefore, the only possible way to deal with large instances of QAP is by taking advantage of heuristics. These heuristic algorithms can obtain a good solution quickly. The most important heuristic approaches used for solving QAP are: simulated annealing [3], genetic algorithm [31], ant colony optimization [13, 29], tabu search [30], greedy randomized adaptive search (GRASP) [22] and scatter search [4].

2 Metaheuristics

In this section, we briefly describe metaheuristics that have been used in our proposed approach. First, we describe the main ideas of the simulated annealing of Connolly [3] and then the “robust tabu search” of Taillard [30] is considered. Next, we explain Fast Ant System (FANT) of Taillard [29]. The source codes for these methods are available on the Internet at http://ina.eivd.ch/collaborateurs/etd/default.html. Finally, a summary of the hybrid genetic algorithm is discussed.

2.1 Simulated annealing

Farhad Djannaty ; Hossein Almasi Department of Mathematics, University of Kurdistan, Sanandaj, Iran



29-31 Aug 2007Intelligent Systems Scientific Society of IranIntelligent Systems Scientific Society of Iran

99--7713861386313

Implementation of Evolutionary Algorithm and Fuzzy Sets for Reliability Optimization of Engineering

Systems

Abstract: This article uses an evolutionary algorithm to solve the series parallel redundancy optimization problem which is in a fuzzy framework. Reliability optimization provides a means to help the reliability engineer achieve such a goal. Most methods of reliability optimization assume that systems have redundancy components in series and / or parallel systems and that alternative designs are available. Optimization concentrates on optimal allocation of redundancy components and optimal selection of alternative designs to meet system requirements. A fuzzy simulation-based evolutionary algorithm is then employed to solve these kinds of fuzzy programming with fuzzy Goal and fuzzy constraints. Finally, numerical examples are also given. Keywords: evolutionary algorithm, reliability analysis, reliability optimization, genetic algorithm, Fuzzy simulation

1 Introduction

As systems have grown more complex , the consequences of their unreliable behaviour have become severe in terms of cost , effort , lives , and so on , and the interest in assessing system reliability and the need for improving the reliability of products and systems have become very important . The reliability of a system can be defined as the probability that the system has operated successfully over a specified interval of time under stated conditions. In the past few decades, the field of reliability has grown sufficiently large to include separate specialized subtopics, such as reliability analysis, failure modelling, reliability optimization, reliability growth and its modelling, reliability testing, reliability data analysis, accelerated testing , and life cycle cost [1].

Reliability optimization provides a means to help the reliability engineer achieve such a goal. Most methods of reliability optimization assume that systems have redundancy components in series and/ or parallel systems and that alternative designs are available. Optimization concentrates on optimal allocation of redundancy components and optimal selection of alternative designs to meet system requirements. In the past two decades, numerous reliability optimization techniques have been proposed. Generally, these techniques can be classified as linear programming, dynamic programming, integer programming, and geometric programming, Heuristic method, Lagrange multiplier, and so on. [2].

M. MOHAMMADI 1,.H. FARAHMAND 2, M. RASHIDINEJAD 2 ,E.ESLAMI3

1Mathematical Department, Islamic Azad University of Najaf abad 2Electrical Engineering Department, Shahid Bahonar University of Kerman, Kerman

3Mathematical Department, Shahid Bahonar University of Kerman, Kerman [email protected]



29-31 Aug 2007



One-sided Process Capability Indices and Fuzzy lower Confidence Bounds for them

M.T. Moeti

Member of Young Researchers Club, Islamic Azad University, Arak branch, Iran [email protected]

M. Mashinchi Faculty of Mathmatics and Computer Sciences, Shahid Bahonar University, Kerman, Iran

[email protected] A. Parchami

Faculty of Mathmatics and Computer Sciences, Shahid Bahonar University, Kerman, Iran [email protected]

Abstract: Process capability indices are used to measure the capability of a process to reproduce items within the specified tolerance preset by the product designers or customers. After introducing fuzzy one-sided process capability indices PUC~ and PLC~ , we obtain fuzzy lower confidence bounds for the introduced indices, where instead of precise quality we have one triangular membership function for one-sided specification limit.

Key words: Lower confidence bound; Fuzzy process capability indices; Ranking function.

1 Introduction

Process Capability Indices (PCIs) pC , pkC and pmC are appropriate for processes with two-sided specification limits (SLs). Some procedures have been developed based on these indices [3, 8, 21 and 22] for the practitioners to use in making decision on whether their processes meet the preset capability requirements. Also, the indices PUC and PLC are designed specifically for processes with one-sided SLs.

After the inception of the notion of fuzzy sets by Zadeh [33], there are efforts by many authors to apply this notion in statistics. For these trends one can see [28, 29, 30]. In quality control topic, where SLs are non-precise

numbers and they are expressed in fuzzy terms, the classical capability indices could not be applied. For such cases Yongting [32] introduced a process capability index pC~ as a real number and it was used by Sadeghpour-Gildeh [27]. Lee investigated a process capability index, pkC , as a fuzzy set [11]. Parchami et al. introduced fuzzy PCIs as fuzzy numbers and discussed relations that governing between them when SLs are fuzzy rather than crisp [15, 18]. Also they obtained fuzzy confidence intervals for these new PCIs and they presented an approach to testing fuzzy PCI [19, 20]. Similarly fuzzy capability indices extended by Moeti et al. where the SLs are L-R fuzzy intervals [16].



29-31 Aug 2007

327


Fuzzy Confidence regions for the Taguchi Index in Fuzzy Process

Z. Ramezani, A. Parchami, M. Mashinchi Faculty of Mathematics and Computer Sciences,

Shahid Bahonar University of Kerman, Kerman, Iran [email protected], [email protected], [email protected]

Abstract: In this paper we present several fuzzy confidence intervals for fuzzy process capability index pmC~ in a fuzzy process based on Roubens ranking function, where we have two membership functions for specification limits. Keyword: Triangular fuzzy numbers, Confidence Interval, Process capability indices, fuzzy statistics, Ranking function. 1. Introduction In the past few years, three major univariate capability indices have been developed and discussed in the literature. They are pC , pkC and

pmC In most cases, the normal distribution and a large sample size are assumed for population of data. Discussion of these process capability indices can be found in [2, 3, 7, 9, 10, 11, 16, 22, 26]. A common method is to use the process capability indices (PCIs) to compare the actual performance of a process to its prior engineering-specified performance. Many papers on PCIs (see, e.g., references listed in [9]) and some books [11] have been published. After the inception of the notion of fuzzy sets by Zadeh [31], there are efforts by many authors to apply this notion in statistics[27]. When, some information of a process are not precise and they are expressed in fuzzy terms, the traditional capability indices could not be applied. For one case a process capability index pC~ as a real number was introduced in [30] and it was used in [24]. A process capability index, pkC~ , as a fuzzy set was introduced in [12]. When specification limits (SLs), are triangular numbers, Parchami et al. proposed fuzzy process capability indices as fuzzy numbers and discussed relations that governing between them when specification limits are fuzzy rather than crisp [18-20]. In this paper we discuss on pmC~ when SLs are triangular fuzzy number. At first we introduce two

estimators for pmC~ and then we obtain various approximate confidence intervals for pmC~ .

2. Preliminary The above introduced traditional PCIs can be classified into two kinds. The first kind deals solely with the process variation in relation to a specified tolerance region. The second kind considers not only the process variation relative to the tolerance region but also the deviation of process mean from target value. The index pC is an example of the first kind and pkC and pmC are of the second kind. In [3] it is pointed out that the exact sampling properties of the estimates of pkC were more complex than the ones for pmC . A process capability index pmC is defined as,

222 )(66)(6 T

LslUslLslUsl

TXE

LslUslCT

pm−+

−=

−=

−

−=

μσσ

That was introduced in [3] and [14], where Lsl and Usl are lower and upper specification limits, respectively, and the target value is

2LslUslT += . Through this paper we suppose that the process of the characteristics follows the normal distribution with mean μ and variance 2σ . Let ℜ be the set of real number. Let

},,,,|{)( ,, cbacbaTF cbaT ≤≤ℜ∈=ℜ where

⎪⎩

⎪⎨

⎧<≤−−<≤−−

=..0

,)/()(,)/()(

,,wo

cxbifbcxcbxaifabax

T cba (1)



29-31 Aug 2007

335


A Method of Generating a Random Sample From a Fuzzy Distribution Function

A. Khorsand 1 , R. Amirzadeh, A. Bozorgnia 2

1A Member of Young Researchers Club,

Islamic Azad University Mashhad Branch, Mashhad, Iran, [email protected]

2 Islamic Azad University Mashhad Branch, Mashhad, Iran,


Abstract: In practical applications, it is very important to generate a random sample or equivalently a sequence of random fuzzy numbers from a fuzzy distribution function. In this paper, we propose fuzzy probability integral trans-formation theorem for fuzzy random variables. As a result of this theorem, we provide a method to generate a sequence of random fuzzy numbers from a fuzzy distribution function. To do this, we use the random fuzzy numbers on [0, 1]. Our attention is on the case where the left and right sides of the membership functions of random fuzzy numbers are quadratic functions. For illustrating the method we give a numerical example.

Keywords: Extension Principle, Fuzzy random variable, probability integral transformation theorem, Random fuzzy number, Triangular shaped fuzzy number. 1 Introduction The topic for statistical inference under fuzzy environment was studied by many researchers. Gebhardt et al. [4], and Taheri [15] gave a good review in this topic. Some authors paid attention to generate a random fuzzy number. A method for generating a random LR fuzzy number was proposed in ([1], [6], [7], [9], [12], [13]). Next, Ferson and Ginzburg [3] provided another way to construct a random triangular fuzzy number. Liu and Chen [11] generated a random triangular fuzzy number and a random trapezoidal fuzzy number. Buckley in [2], proposed another method to produce a random triangular shaped fuzzy number, where the left and right sides of the membership functions of fuzzy numbers are quadratic functions. All of these methods are based on crisp random variables. Our motivation is based on fuzzy random variables. The concept of fuzzy random variables was introduced by Kwakernaak [10] and Puri and

Ralescu [14]. Wu [16] considered the construction of the fuzzy distribution function of fuzzy random variables using a family of closed intervals. In this paper, we propose fuzzy probability integral transformation theorem for fuzzy random variables. Then we provide a method of generating a random sample from an arbitrary fuzzy distribution function. Our random fuzzy numbers will have random base. We believe this method gives a better picture of random fuzzy numbers. The organization of this paper is as follows. In section 2, we give a brief review of fuzzy random variables. In section 3, we propose fuzzy probability integral transformation theorem and its inverse for fuzzy random variables. We provide a method of generating a random sample from an arbitrary fuzzy distribution function, in section 4. The final section is the conclusion part. An illustrative example is given to clarify the method.



29-31 Aug 2007

363

Fuzzy linear regression analysis with trapezoidal coefficients

T. Razzaghnia ∗,1 , E. Pasha 2 , E. Khorram 3 , A. Razzaghnia 3

1 Department of Statistics, Islamic Azad University, Roudehen Branch, Tehran, Iran.

2 Department of Mathematics, Teacher Training University, Tehran, Iran. 3 Faculty of Mathematics and Computer Science, Amirkabir University of Technology, Tehran, Iran. ∗ E-mail: [email protected].

Abstract : In this paper, we aim to extended the constraints of Tanaka’s model. Applied coefficients of the fuzzy regression by them is the symmetric triangular fuzzy numbers, while we try to replace it by more general asymmetric trapezoidal one. Possibility of two asymmetric trapezoidal fuzzy numbers is explained by possibility distribution. Two different models is presented and a numerical example is given in order to compare the proposed models with previous one. Error values shows advantage of the presented models with respect to constraints of Tanaka’s model. Keywords: Fuzzy numbers, Fuzzy linear regression, Possibility distribution, Mathematical programming. 1. Introduction Fuzzy linear regression was proposed by Tanaka et al. [17] in 1982. Many different fuzzy regression approaches have been proposed by different researchers since then, and also this subject has drawn much attention from more and more people concerned. In general, there are two approaches in fuzzy regression analysis: linear programming-based method [6,11,16,17] and fuzzy least squares method [1,2,3,4,7,10,12,13,14].The first method is based on minimizing fuzziness as an optimal criterion. The second method used least-square of errors as a fitting criterion. The advantage of first approach is its simplicity in programming and computation, while that the degree of fuzziness between the observed and predicted values is minimized by using fuzzy least squares method. Tanaka et al.[17] regarded fuzzy data as a possibility distribution, the deviations between the observed values and the estimated values were

supposed to be due to fuzziness of system structure. This structure was represented as a fuzzy linear function whose parameters were given by fuzzy sets. They resorted to linear programming to develop their regression model. In [17], the coefficients of the fuzzy regression are symmetric triangular fuzzy numbers. In this paper, we explain limitations of these methods and we extended the symmetric triangular fuzzy coefficients to asymmetric trapezoidal fuzzy numbers. Also we use possibility distribution for asymmetric trapezoidal fuzzy numbers and we prove a theorem about possibility of two asymmetric trapezoidal fuzzy numbers. The paper is organized as follows. In section 2, some elementary properties of fuzzy numbers and fuzzy linear regression are described. The propose method is presented in section 3. A numerical example is illustrated to compare the proposed method with previous ones, in section 4.



29-31 Aug 2007


Abstract: The aim of this paper is to define the probability on some newly defined balanced lattices. Then we will find the formula of the defined probability on these balanced lattice. Keywords: fuzzy set, balanced set, balanced lattice, probability on a lattice. 1 Introduction The paper presents two newly defined balanced lattices bL and *

bL . It investigates the probability on these lattices. The definitions of balance lattices L , *L and the probability on them are reminded in section 2. At last section,

bL and *bL will be introduced and the

probability on them is discussed. The exact formula of the probabilities on these lattices are found. 2 Preliminaries In this section we review some notions that we need through this paper. 2.1 Balanced sets A classical fuzzy set A in a universe X can be defined in terms of its membership function

[ ]: 0,1A Xµ → . Membership functions, by analogy to characteristic functions, define fuzzy connectives: union, intersection and complement. The definitions are expressed, as in the case of the crisp sets, by max, min and complement to 1.

One can observe an asymmetry of the set of values of characteristic function and membership functions: if the state of (certain) inclusion of an element is denoted by 1, the state of (certain) exclusion might be denoted by -1, rather than 0. This observation would be worthless since most of studies of fuzzy set operators and all operators defined on crisp sets have been valued in the unit interval [0,1]. Moreover, both scales: unipolar, with the unit interval [0,1], and biopolar, with the symmetric interval [-1,1] , are indistinguishable in the meaning of the linear mapping ( ) 2 1i x x= − . See [1]. 2.2 The lattices *L and L Definition 2.2.1 [4] The lattice L is the set

( ) ( ) [ ]{ }2, , 0,1x y x yL = ∈ ,

with the order ( ) ( )1 1 2 2 1 2 1 2, , & .Lx y x y x x y y≤ ⇔ ≤ ≥

We denote its units by ( )0 0,1L = and

( )1 1,0L = . See Figure 1. Theorem 2.2.2 [4] ( ), LL ≤ is a complete lattice.

1

1

L

Figure 1: The lattice L

Probability on balanced lattices

M. Saeb and M. Mashinchi Faculty of Mathematics and Computer Sciences

Shahid Bahonar University of Kerman , Kerman , Iran [email protected] , [email protected]




Dp;q�DISTANCE AND THE STRONG LAW OF LARGENUMBER FOR NEGATIVELY DEPENDENT FUZZY

RANDOM VARIABLES

B. Sadeghpour Gildeh and R. ZamanDepartment of Statistics, University of Mazandaran, Babolsar, Iran

[email protected]

Abstract :In this paper, we extend strong lawsof large numbers (SLLN) of real random vari-ables to negatively dependent fuzzy randomvariables.

Key words: Fuzzy numbers; Fuzzy set-valued random variables; Negatively depend-ent; Pairwise negatively dependence; Thestrong law of large numbers.

1 Introduction

The concept of dependence permeates ourEarth and its inhabitants in a most profoundmanner. The last thirty years of the 20thcentury have witnessed a rapid resurgence ininvestigations of dependence properties fromstatistical and probabilistic points of view Joe[5]. Limit theorems on real-valued dependentrandom variables have been extended in the lit-erature Lehman and E.L. [7]. With the devel-opment of the theory and application of fuzzyset, the study of fuzzy set-valued random vari-ables was initiated by several authors, in par-ticular Puri and Ralescu [9] introduced the no-tion of fuzzy random variables. The limit the-orems on independent fuzzy random variables,for example the strong law of large numbers(SLLN) for sums of independent fuzzy random

variables, have been studied by several people.Y. Feng [3] provided a good review about SLLNof fuzzy random variables.The main purpose of this paper is extending

SLLN theorems of negatively dependent real-valued random variables to negatively depend-ent fuzzy random variables. In section 2, werecall some basic concepts of fuzzy numbers. Insection 3, the de�nition negatively dependentfuzzy random variables have been presented,and �nally, in section 4 we prove some theor-ems on the convergence of a sequence on negat-ively dependent fuzzy random variables basedon Dp;q-distance.

2 Preliminary

In this section we �rst recall some notions offuzzy sets, fuzzy numbers and some operationson fuzzy numbers. And then we present Dp;q-distance de�ned on the space of fuzzy numbers[10].De�nition 2.1 ([10]) Let E be a universalset, then a fuzzy set eA of E is de�ned by itsmembership function eA : E ! [0; 1]. For allx 2 E , eA(x) is the membership grade of x toeA.De�nition 2.2 ([10]) A� is called the � �

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Reducible Fuzzy Markov Chainand Fuzzy Absorption Probability

B. Sadeghpour Gildeh and A.DadgarDepartment of Statistics, University of Mazandaran, Babolsar, Iran

[email protected]

Abstract : In this paper Markov chains withfuzzy states are considered.The main objectiveis to study reducibility of a Markov chain withfuzzy states.It is shown that if the Markov chainassociated with the process of non-fuzzy statesis reducible the corresponding Markov chain as-sociated with the process of fuzzy states is notnecesserily reducible. After presenting defe-nition of absorbing fuzzy state and transientfuzzy state we show how absorbing fuzzy statesare constructed.Then we prove a relation aboutprobability of absorpaition from transient stateto an absorbing class, and illustrait it with ex-amples.

Keywords: Markov chain, fuzzy state ,reducible, absorption probability, absorbingstate, transient state.

1. IntroductionIn a seminal paper Bellman and Zadeh [1]

�rst studied a fuzzy decision process.The au-thors consider stochastic systems in afuzzy en-vironment.The fuzzy Markov chains have a po-tential application in fuzzy Markov algorithmsproposed by Zadeh in [8]. There have been afew other papers published on fuzzy Markovchains . In [5] the elements in trasition matrixare fuzzy proabilities. The paper [7] is about aMarkov fuzzy process with a transition possi-bility measure in an abstract state space. In [3]

both the state and action are fuzzy, the transi-tion of states is de�ned using a fuzzy relation.In [2] a Markovian decision process with fuzzystate is considerd.In this paper we consider absorbing and

transient fuzzy class in fuzzy Markov chains.Fuzzy states occur essentially in two kinds ofsituations. First where the states of the sys-tem cannot be percisely measured and thus thestates used to model the system are intrinsi-cally fuzzy. While in the second kind of situ-ations, the actual states can be exactly mea-sured and are observable, but the number ofstates is so large that the decisions are not as-sociated with the exact states of the system.In these situations, the decisions are associatedwith fuzzy states which can be de�ned as fuzzysets on the original non-fuzzy state space of thesystem.

2. PreliminaryIn this section we recall some de¢ nitions

of fuzzy Markov chain and the probability offuzzy event.De�niton 2.1. [2] A �nite Markov chain fXng

is a Markov stochastic process whose statespace is a �nite set S = fs1;:::;sMg. Theproability of Xn+1 = sj when Xn = si isdenoted by pij = Pr(Xn+1 = sj jXn = si ).P = (pij)M�M is called the transition matrix

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، دانشگاه فردوسي مشهد ، دانشگاه فردوسي مشهد13861386 شهريور شهريور 77--99 ، ، فازيفازيتمين كنفرانس سيستمهاي تمين كنفرانس سيستمهاي ففهه389

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Fuzzy Traffic Rate Controller (FTRC) for Mobile Ad hoc Network Routers

Masood Niazi Torshiz

Islamic Azad University-Mashhad branch Khavaran Higher Education of Institute, Mashhad, Iran

E-mail:[email protected]

Abstract: Characteristics of mobile ad hoc networks such as lack of central coordination, mobility of hosts, dynami-cally varying network topology, and limited availability of resources make QoS provisioning very challenging in such networks. The FTRC consists of two sections. The first section, which is Fuzzy AIMD, uses additive increase multiplica-tive decrease (AIMD) rate control algorithm as base. In AIMD, the node increments its transmission rate with increment rate of c Kbps and decreases its transmission rate by r percent. Fuzzy AIMD accepts the packet delay and the "delay-threshold d" as inputs and calculates the c and r by using a set of fuzzy rules. The second section is Fuzzy Regulation, which selects a set of flows that have a major part in causing congestion, and notifies the corresponding sources to re-duce their sending rates. The selection of flows is done according to the parameters "flow priority" and "the difference between actual rate and agreed rate". Keywords: QoS, Mobile Ad hoc Network, Fuzzy Control, Traffic Management 1. Introduction Mobile ad hoc networks are autonomous dis-tributed systems that comprise a number of mo-bile nodes connected by wireless links forming arbitrary time-varying wireless network topolo-gies [1-3]. Mobile nodes function as hosts and routers. As hosts, they represent source and des-tination nodes in the network, while as routers, they represent intermediate nodes between a source and destination, providing store-and-forward services to neighboring nodes. Nodes that constitute the wireless network infrastruc-ture are free to move randomly and organize themselves in arbitrary fashions. Therefore the wireless topology that interconnects mobile hosts/routers can change rapidly in unpredict-able ways or remain relatively static over long periods of time [4-6]. In addition to being bandwidth constrained, mobile ad hoc networks are power constrained because network nodes rely on battery power for energy. Providing suit-able quality of service (QoS) support for the de-livery of real-time audio, video and data in mo-bile ad hoc networks presents a number of sig-nificant technical challenges [7-11]. The FTRC uses AIMD rate control algorithm as base, in which, each node increases its transmis-

sion rate with increment rate of c Kbps and de-creases its transmission rate by r percent. FTRC accepts the packet delay and the differentiated delay as inputs and calculates the parameters c and r by using a set of fuzzy rules. Fuzzy Regulation module selects a set of flows that have a major part in causing congestion, and notifies the corresponding sources to reduce their sending rates. The selection of flows is done according to the parameters "flow priority" and "the difference between actual rate and agreed rate". Fuzzy regulation module computes the probability of selecting a flow to be a mem-ber of this set. The rest of this paper is organized as follows. In section 2 we describe the proposed fuzzy AIMD in detail. The proposed Fuzzy regulation algo-rithm is explained in Section 3. In Section 4, we evaluate the performance of the Fuzzy AIMD and Fuzzy Regulation mechanisms via computer simulation. Section 5 concludes the paper. 2. Fuzzy AIMD The AIMD rate control algorithm determines the departure rate of the traffic shaper according to the packet delay feedback. The typical AIMD rate control algorithm works as follows. Every T seconds, each node increases its transmission



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397

A Fuzzy Routing Algorithm for Low Earth Satellite Networks

Boshra Rajaee, Mohammad Hossein Yaghmaee Ferdowsi Univercity of Mashhad

Mashhad, Iran [email protected] ,[email protected]

Abstract : Low Earth Orbit (LEO) satellite networks have dynamic, yet deterministic topologies. Because of dynamic characteristics would result in the re-routing all connections that are passing through a turned off link. But on the other hand, because of deterministic characteristics, we have some useful information about future of network. In this paper we attempt to develop an algorithm to reduce the number of re-routings by assigning routes that are more permanent. This is done by using a fuzzy system that before routing assigns weights to all links based on their handover time and residual bandwidth. Performance of algorithm is investigated using simulation experiments. Keywords: Satellite networks, LEO, routing, fuzzy, handover. 1. Introduction

Low earth orbit (LEO) satellite systems can provide users with low-cost and truly global wireless services, regardless of user locations [1]. Hence, there has been a lot of recent interest in developing efficient schemes for channel allocation and handoff in such systems. LEO satellite systems have certain unique features not found in other satellite and ground-based wireless communication systems. We list some of them here.

While geo-synchronous satellites orbit earth at an altitude of about 36,000 km, LEO satellites orbit earth in the 500–2000 km altitude range. Besides reducing the propagation delay suffered by signals, the lower orbital altitude also means a lower power requirement at the hand-held terminals, thus improving the portability of the terminal.

A large number of satellites will be required to ensure that there is always at least one satellite in view for every location on earth. For example, the IRIDIUM system (the target system in our research) uses a 66-satellite network to provide global coverage. A typical LEO satellite system will consist of a number of low-earth orbits with a fixed number of satellites traversing each orbit.

Another unique feature of LEO satellites is due to the fact that they are not in geo-synchronous orbit, and hence will not appear stationary to a stationary observer on earth. In addition to Up Down Links (UDL), the Inter-Satellite Link (ISL) also changed based on the distance and viewing angel between them.

Changes of UDL and ISL connectivity’s result in a dynamic network topology with challenging routing problems. Any connection that is through a connection that will be turned off may be re-routing. If the number of connections that need to be re-routed due to link handover is large, this will cause signaling overhead in network. Moreover, handover calls may be blocking during the re-routing process, that is not desirable.

A protocol for routing in LEO satellite networks has been developed in [2], that is called Probabilistic Routing Protocol (PRP). During the routing phase of a newly arriving call, the PRP eliminates the links that will be turned off before the call releases the link due to call termination or connection handover. Since the algorithm has no knowledge of the call duration or exact terminal location, route usage time is only known probabilistically. The probability distribution function of the route usage time of the call is determined to realize algorithm. Our purpose in this research is to delete the need for call statistics



29-31 Aug 2007



A metaheuristic Algorithm for New Models of Fuzzy Bus Terminal Location Problem with a Certain Ranking Function

[email protected], [email protected], [email protected] Abstract: Bus network design is an important problem in public transportation. In real word, some parameters of this problem are uncertain. We introduce two new models for bus terminal location with fuzzy parameters. In the first formulation, the number of possible passengers corresponding to each node is a fuzzy number. In the second formulation, an additional assumption of fuzzy neighbourhood is considered. These problems being NP-hard, we use the genetic algorithm with a newly designed crossover operator for solving them. Results of computational experiments demonstrating the efficiency of the proposed algorithm are reported. Keywords: Fuzzy bus network, location problem, ranking function, genetic algorithm. 1 Introduction Bus network design is an important problem in public transportation. The main step of the design is determining the number of required terminals and their locations. This is a special type of facility location problem, an NP-hard combinatorial optimization problem [14]. Consider a set F of potential facilities, each with a setup cost ( )c F , and let U be a set of users (or costumers) who must be served by these facilities. The cost of serving user u with facility f is given by the distance ( ),d u f between them (often referred to as service cost or connection cost as well). The facility location problem consists of determining a set S F⊆ of facilities to be located so as to minimize the total cost (including setup and service) of covering all the customers:

( ) ( ) ( )cos min , .f Sf S u U

t S c f d u f∈∈ ∈

= +∑ ∑ (1.1)

Note that we assume each user is allocated to the closest open facility. For location problems, it is usually assumed that exact data are known. However, in real applications, location problems can be appropriately modelled using fuzzy parameters (some fuzzy location problems can be seen in [4, 5,

6, 7, 16, 18, 19]). This paper is organised as follows. In Section 2, we give two new formulations for the fuzzy bus terminal location problem (FBTLP) as fuzzy integer programming problems [12]. Then, after stating some properties of fuzzy numbers in Section 3, we explain adoption of the genetic algorithm (GA) for both formulations in Section 4. Finally, in Section 5, we test an implementation of our proposed algorithm on some test problems, and demonstrate the efficiency of the algorithm by the numerical results obtained. In Section 6, we conclude and give suggestions for further research. 2 Two Formulations of the FBTLP For stating the crisp formulation of the FBTLP [1], we consider a set of nodes (by their coordinates) in a city. We suppose that the number of enter and exit of passengers in every node (that is called the potential of the node) is available. Also, we suppose that if a node is accepted as a bus terminal, it can service the other nodes that are located in its neighbourhood. So, we want to select an optimal subset with k members from the set of candidate nodes for dedicating bus terminals. Below, we list the parameters of FBTLP.

:J The set of nodes to receive service. :I The set of candidate nodes for bus terminals.

S. Babaie-Kafaki, R. Ghanbari and N. Mahdavi-Amiri Department of Mathematical Sciences, Sharif University of Technology, Tehran, Iran



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471

Finding the Inversion of a Square Matrix and Pseudo-inverse of a Non-square Matrix by Hebbian Learning Rule

Abstract: In this paper, we discuss a neural network based on hebbian learning rule for finding the inverse of a matrix. First we described finding the inverse of a matrix by mentioned neural network. Finally, experimental results for square and non-square matrices are presented to show the effectiveness of the approach. Proposed method is also scalable for finding the inversion of large-scale matrices. Keywords: Hebbian Learning rule, neural networks, solving simultaneous linear equations 1 Introduction Finding the inversion of a matrix is considered to be one of the basic problems widely encountered in science and engineering since it is frequently used in many applications (e.g. robotics, signal processing, Wiener and Kalman filtering). In many applications an on-line (e.g. real time) inversion of a matrix is desired. In monitoring and control of dynamic systems, there is often a need for finding a real-time matrix inversion of a large-scale matrix. If such a large-scale problem needs to be solved in real time, existing numerical methods and sequential techniques may not scale well. There are a variety of methods for matrix inversion, usually classified as direct and iterative. Direct methods are distinguished by the Fact that they find the correct solution in a finite number of operations. Iterative methods are characterized by an initial estimate of the solution, and subsequent update of the estimate based on the previous estimate and some error measure. Iterative algorithms are sometimes preferred, especially in problems of medium/large size [7]. Finding the inversion of a matrix with constant and time varying coefficients has been studied in the field of neural networks [1, 2, 3] with varying results in a highly parallel fashion. Recurrent

Neural Network (RNN) and neural networks with perceptron learning rule were studied to find matrix inversion. RNN (i.e. continuous approach) recovers its inputs to find matrix inversion while in the neural networks with perceptron learning rule (i.e. discontinuous approach), the matrix weight is updated until all the outputs of neurons are same as desire ones. In this paper, a one-layer neural network that updates its weights by hebbian learning rule was applied for inverting of square and nonsquare matrices. Hebbian learning rule is one of the first unsupervising learning rules of neural networks and it is the base of all rules used for associative neural networks. This rule first proposed by Donald Heb in 1949 [5]. The rest of the paper is organized as follows: Section 2 presents problem formulation, while the neural network model and hebbian learning rule for inverting of matrices is presented in section 3 with experimental results discussed in section 4. 2 Problem Formulation to Find matrix Inversion 2.1 A is a square Matrix

Zeinab Ghassabi, Ali Khaki-Sedigh Tehran Azad University, Science and Research Branch, KNTU




29-31 Aug 2007



Solving Fuzzy Integral equations by Differential Transformation Method

Y. Nejatbakhsh T. Allahviranloo N. A. Kiani Islamic Azad University Islamic Azad University Islamic Azad University Firouzkooh Branch Science and Research Branch Science and Research Branch Department of Applied Mathematics Department of Applied Mathematics Department of Applied Mathematics Tehran; Iran Tehran; Iran Tehran; Iran [email protected] [email protected] [email protected] Abstract: In this paper, we are going to solve Fuzzy integral equations (FI)s by differential transformation method(DTM). Intrinsically, DTM evaluates the approximating solution by the finite Taylor series. The differential transformation method does not evaluate the derivative symbolically; instead, it calculates the relative derivatives by an iteration procedure described by the transformed equations obtained from the original equations using differential transformation. The proposed method provides the Taylors series expansion solution for the domain between any adjacent grid points. Some numerical examples are given to illustrated the proposed extension of DTM to solve fuzzy Fredholm integral equations. Key–Words: Differential transformation, one dimensional Volterra integral equations, Numerical treatments Fuzzy integral Equations, Fuzzy number.

1 Introduction Fuzzy set theory is a powerful tool for modeling uncertainty and for processing vague or subjective information in mathematical models. Their main direction of development have been diverse and its application to the very varied real problems, for instance in the golden mean [5], Practical systems [8], quantum optics and gravity [9], synchronize hyperchaotic system [10], medicine [1], engineering problems. The topics of fuzzy differential equations (FDE) and fuzzy integral equations (FIE) which attracted growing interest for some time, in particular in relation to fuzzy control, have been rapidly developed in recent years. The first step which included applicable definitions of the fuzzy derivative and the fuzzy integral was followed by introducing FDE and FIE and establishing sufficient conditions for the existence of unique solutions to these equations. Finally, numerical algorithms for calculating approximates to these solutions were designed. Prior to discussing fuzzy differential and integral equations and

their associated numerical algorithms, it is necessary to present an appropriate brief introduction to preliminary topics such as fuzzy numbers and fuzzy calculus. The concept of fuzzy sets which was originally introduced by Zadeh [11] led to the definition of the fuzzy number and its implementation in fuzzy control [4] and approximate reasoning problems [12, 13]. The basic arithmetic structure for fuzzy numbers was later developed by Mizumoto and Tanaka [14, 15], Nahmias [16], Dubois and Prade [17, 18], and Ralescu [19], all of which observed the fuzzy number as a collection of alevels, 10 ≤≤ ct [20]. Additional related material can be found in [21, 22, 23, 24, 25, 27, 28, 29, 30, 31, 32]. The fuzzy mapping function was introduced by Chang and Zadeh [5]. Later, Dubois and Prade[6] presented an elementary fuzzy calculus based on the extension principle [11]. Puri and Ralescu [33] suggested two definitions for fuzzy derivative of fuzzy functions. The first method was based on the H-difference notation and was



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29-31 Aug 2007

FUZZY TOPOLOGICAL SPACES

ALIREZA KAMEL MIRMOSTAFAEE1

Abstract. In this paper, we discuss about various definitions of fuzzy topological

spaces. Some obstacles which appear in theory of fuzzy topological spaces will be dis-

cussed.

1. introduction

The concept of a fuzzy set, which was introduced by Zadeh in [4] motivated some

authors to generalizing many concepts of general topology to fuzzy topological space. In

this paper, we investigate some of these results to find more appropriate definition of a

fuzzy topology on a space, which gives generalization of basic concepts of topology such

as open sets, neighborhoods, continuity and compactness.

2. Fuzzy topology

We begin with several preliminary definitions.

Let X be a set, by a fuzzy set in X we mean a function µ : X → [0, 1]. In fact,

µ(x) represents the degree of membership of x in the fuzzy set X. For example, every

characteristic function of a set, is a fuzzy set. The characteristic functions of subsets of a

set X are referred to as the crisp fuzzy sets in X.

Let A and B be fuzzy sets in a space X, with the grades of membership of x in A and B

denoted by µA(x) and µB(x), respectively. Then we say that

(1) A = B if and only if µA ≡ µB.

(2) A ⊂ B if and only if µA ≤ µB.

(3) C = A ∪B if and only if µC ≡ max{µA, µB}.(4) D = A ∩B if and only if µD ≡ min{µA, µB}.(5) E = A′ if and only if µE ≡ 1− µA.

Key words and phrases. Fuzzy topology.1



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COMMON FIXED POINT THEOREM IN COMPLETE FUZZYMETRIC SPACES

SHABAN SEDGHI

——————————————————————————————————–

Abstract. In this paper, we establish a common fixed point theorem in com-

plete fuzzy metric spaces which generalizes some results in [15].

——————————————————————————————————–

1. Introduction and Preliminaries

The concept of fuzzy sets was introduced initially by Zadeh [17] in 1965. Sincethen, to use this concept in topology and analysis many authors have expansivelydeveloped the theory of fuzzy sets and application. George and Veeramani [5]and Kramosil and Michalek [8] have introduced the concept of fuzzy topologicalspaces induced by fuzzy metric which have very important applications in quantumparticle physics particularly in connections with both string and ε(∞) theory whichwere given and studied by El Naschie [1, 2, 3, 4, 16]. Many authors [6, 10, 11, 12, 13]have proved fixed point theorem in fuzzy (probabilistic) metric spaces.

Definition 1.1. A binary operation ∗ : [0, 1] × [0, 1] −→ [0, 1] is a continuoust-norm if it satisfies the following conditions

(1) ∗ is associative and commutative,(2) ∗ is continuous,(3) a ∗ 1 = a for all a ∈ [0, 1],(4) a ∗ b ≤ c ∗ d whenever a ≤ c and b ≤ d, for each a, b, c, d ∈ [0, 1].

Two typical examples of continuous t-norm are a ∗ b = ab and a ∗ b = min(a, b).

Definition 1.2. A 3-tuple (X, M, ∗) is called a fuzzy metric space if X is anarbitrary (non-empty) set, ∗ is a continuous t-norm, and M is a fuzzy set onX2 × (0,∞), satisfying the following conditions for each x, y, z ∈ X and t, s > 0,

(1) M(x, y, t) > 0,(2) M(x, y, t) = 1 if and only if x = y,(3) M(x, y, t) = M(y, x, t),(4) M(x, y, t) ∗M(y, z, s) ≤ M(x, z, t + s),(5) M(x, y, .) : (0,∞) −→ [0, 1] is continuous.

Let (X, M, ∗) be a fuzzy metric space . For t > 0, the open ball B(x, r, t) withcenter x ∈ X and radius 0 < r < 1 is defined by

B(x, r, t) = {y ∈ X : M(x, y, t) > 1− r}.

2000 Mathematics Subject Classification. 54E40; 54E35; 54H25.Key words and phrases. Fuzzy contractive mapping; Complete fuzzy metric space.The corresponding author: sedghi [email protected] (Shaban Sedghi Ghadikolaee).

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Signed Decomposition of Fully Fuzzy Linear

Systems

Nasser Mikaeilvand (a)∗ Tofigh Allahviranloo (b)

(a)Department of Mathematics, Ardabil Branch, Islamic Azad University, Ardabil, Iran.(b) Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran,

Iran.

Abstract

In this paper, we discuss fully fuzzy linear systems in the formAX = b (FFLS). A novel method for finding the non-zero fuzzysolutions of these systems is proposed. We suppose that all elementsof coefficient matrix A are positive and we employ parametric formlinear system and finally, Numerical examples are used to illustratethis approach and compare its results with another methods.

keywords: Fuzzy numbers, Fully fuzzy linear systems, Systems offuzzy linear equations, Non-zero solutions.

1 Introduction

Systems of linear equations are used to solving many problems in variousarea such as structural mechanics applications in civil and mechanical struc-tures, heat transport, fluid flow, electromagnetism,.... In many applications,at least one of the system’s parameters and measurements are vague or im-precise and we can present them with fuzzy numbers rather than crisp num-bers. Hence, it is important to develop mathematical models and numericalprocedure that would appropriately treat general fuzzy system and solvethem.

The system of linear equations AX = b where the elements, aij , of thematrix A and the elements, bi, of the vector b are fuzzy numbers, is calledFully Fuzzy Linear System (FFLS).

The n×n(FFLS) has been studied by many authors [2, 3, 4, 7, 8, 15, 16,17, 18, 19, 20, 21]. Buckly and Qu in their continuous work [2, 3, 4] suggested

∗Corresponding author Email: [email protected]

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29-31 Aug 2007

Iteration approach of solving interval and fuzzy

linear system of equations

M. Adabitabar Firozja ∗

Department of mathematics, Qaemshahr Branch, Islamic Azad University, Qaemshahr, Iran.

Abstract

In this paper, first norm of interval vectors is defined and then itis extended to norm of fuzzy number vectors. Finally is applied forsolving the system of linear equations as X = AX + b that A is a realn× n matrix and b is a interval or fuzzy vector.

Keywords: Metric Distance; Fuzzy Numbers; Norm; Linear equation.

1 Introduction

Xizhao et al. [3] introduced the iteration algorithms for solving this prob-lems by metric distance subject to ‖A‖∞ < 1 but we solve them subject to‖A‖1 < 1. The paper is organized as follows: Fuzzy background is presentedin section 2. The proposed norm of interval vector and interval matrix arediscussed in section 3. The proposed norm of fuzzy vector and fuzzy matrixare discussed in section 4. Iteration approach for solving the system of linearequations as X = AX + b is introduced in section 5. Finally, conclusion isdrawn in Section 6.

2 Fuzzy Background

A fuzzy set A = (a1, a2, a3, a4) is a generalized left right fuzzy numbers(GLRFN) of Dubois and Prade [2], if its membership function satisfy in thefollowing:

µA(x) =

L( a2−x

a2−a1), a1 ≤ x ≤ a2,

1, a2 ≤ x ≤ a3,R( x−a3

a4−a3), a3 ≤ x ≤ a4,

0, otherwise

(1)

Where L and R are strictly decreasing functions defined on [0, 1] and satis-fying the conditions:

L(t) = R(t) = 1 if t ≤ 0L(t) = R(t) = 0 if t ≥ 1

(2)

∗Corresponding author: M. Adabitabar Firozja E-Mail: [email protected]

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FUZZY BANACH ALGEBRA

I. SADEQI AND A. AMIRIPOUR

Abstract. In this paper first we show that there is a logical gap on the fuzzy norm

which is used in the theorem (1.2) in [2] so that this theorem in [1] and all related theorems

assumed in [1] and [2]do not hold true . Then we revise and correct the definition of

fuzzy function N(x, t) to get a fuzzy norm in the theorem (1.2) in [2]. By using the

revised fuzzy norm in the theorem (2.6) instead, the theorem and all related results will

remain true. We also give the definition of fuzzy Banach algebra and get some results.

1. Introduction

Our notations and definitions follow [1]. Let X be a vector space, a fuzzy subset N of

X×R is called a fuzzy norm on X if the following conditions are satisfied for all x, y ∈ X

and c ∈ R:

(N1) N(x, t) = 0 for all non-positive real number,

(N2) N(x, t) = 1 for all t ∈ R+ if and only if x = 0

(N3) N(cx, t) = N(x, t|c|), for all t ∈ R+and c 6= 0

(N4) N(x + y, t + s) ≥ min{N(x, s), N(y, t)}, for all s, t ∈ R

(N5) N(x, .) is a non -decreasing function on R, and supt∈R N(x, t) = 1.

The pair (X, N) is said to be a fuzzy normed space.

As an example of fuzzy normed space let (X, ‖ ‖) be a normed space. Define,

N(x, t) =

{0 t ≤ ‖x‖1 t > ‖x‖

Then one can easily check that (X, N) is a fuzzy normed space. For more examples of

the fuzzy normed space see the papers [1] and [2].

In [1], the author has constructed α-norms by using the concept of fuzzy norms and vice

versa. Also by applying the α-norms on the normed space, they proved that F (X, Y ), the

space of all fuzzy bounded operators from the fuzzy normed space (X, N1) to the fuzzy

normed space (Y,N2), is a fuzzy normed space. Since bounded operators have crucial

1Corresponding author

Date: March 11, 2007.

Key words and phrases. fuzzy normed space, fuzzy bounded operator.1



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Some Properties of Zariski Topology onthe Spectrum of Prime Fuzzy

Submodules

R. Mahjoob, R. AmeriMathematics Department, Faculty of Basic Sciences University of Mazandaran

Babolsar-Iran

e-mail: [email protected], [email protected]

Abstract

Let R be a commutative ring with identity and let M be an R-module.We topologize FSpec(M), the collection of all prime Fuzzy submodules of M ,analogous to that for FSpec(R), the spectrum of fuzzy prime ideals of R, andinvestigate the properties of this topological space.

Keywords: prime Fuzzy submodules, fuzzy prime spectrum, L-top modules , Zariskitopology.

1 Introduction

Let R be a commutative ring with identity and M be a unitary R-module. Theprime spectrum Spec(R) and the topological space obtained by introducing Zariskitopology on the set of prime ideals of a commutative ring with identity play animportant role in the fields of commutative algebra, algebraic geometry and latticetheory. Also, recently the notion of prime submodules and Zariski topology onSpec(M), the set of all prime submodules of a module M over a commutative ringwith identity R, are studied by many authors ( for example see [11-14] ). As it iswell known Zadeh introduced the notion of a fuzzy subset µ of a nonempty set Xas a function from X to unit real interval I = [0, 1]. J. E. Goguen in [5] replaced Iby a complete lattice L in the definition of fuzzy sets and introduced the notion ofL-fuzzy sets. Fuzzy submodules of M over R were first introduced by Negoita andRalescu [17]. Pan [21] studied fuzzy finitely generated modules and fuzzy quotientmodules.

In the last few years a considerable amount of work has been done on fuzzy idealsin general and prime fuzzy ideals in particular, and some interesting topologicalproperties of the spectrum of fuzzy prime ideals of a ring are obtained (see [4, 6-10]).

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29-31 Aug 2007

A NEURAL NETWORK MODEL FOR SOLVING STOCHASTICFUZZY MULTIOBJECTIVE LINEAR FRACTIONAL PROGRAMS

S. EFFATI 1, H. SADOGHI2, Z. SABERI 1

Abstract. The paper deals with stochastic fuzzy multiobjectives linear frac-

tional programs. It is transformed to its equivalent deterministic crisp multiob-

jective linear program by using a modified possibility programming approach.

Then is converted to a neural network model. Our linear neural network is

able to generated optimal solutions. We solve neural network model with one

of numerical method.Finally, simple numerical examples are provided for the

sake of illustration.

1. Introduction.

The chance-constrained approach and the possibility programming technique,that has been stated by Negi and Lee [1] and modified by Iskander [2], are utilized totransform the suggested program to its equivalent deterministic-crisp multiobjectivelinear program in the case of exceedance possibility or the case of strict exceedancepossibility[3]. In this paper we use neural network for solving the stochastic fuzzymultiobjective linear fractional program . Recently, several new dynamic solversusing artificial neural network models have been developed .See e.g.Tank and Hop-field (1985), Kennedy and Chua (1987), Rodriguez-Vazquez et al(1990), Wu et al(1996), Xia et al(2002), Effati(2006).In the present paper, one neural network model for a stochastic fuzzy multiobjectivelinear fractional program is converged to real solutions.

2. Problem Formulation

In general, consider a stochastic fuzzy multiobjective linear fractional program-ming problem of the following form:

(2.1) Maximizecr1x1 + . . . + crnxn + cr0

dr1x1 . . . + drnxn + dr0, r = 1, . . . , p,

Key words and phrases. Possibility programming,Chance-constrained,Stochastic fuzzy multi-

objective linear fractional programs, Neural networks.

1



xN

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Application of a hybrid GA-BP optimized neural network for springback estimation in sheet metal forming process

Abstract: There is a small but important deviation in sheet metal bending between the component angle and tool angle after unloading because of springback, i.e. elastic deformation. Since springback is unavoidable, the precision and reliability of products and subsequent assembly operations are severely affected. As a result of this lack of robustness intelligent technologies have received much attention in a wide range of metal-forming applications. Developments in faster computation techniques have made artificial neural networks (ANNs) and genetic algorithms (GA), very popular choices in modelling of sophisticated phenomenon. The present work, in order to construct the estimation model of springback, intends to integrate ANN with a hybrid genetic algorithm-back propagation (GA-BP) training method to determine appropriately the weights of neural network, making up for the defects of back propagation (BP) algorithm. In this paper, based on the available Experiments, three automotive body alloys using a range of die radius, friction coefficients and controlled tensile forces in a draw-bend process are considered. By using the developed estimation model further study on the relation of springback and various process parameters are carried out. Keywords: Springback, Prediction, Metal forming, Neural network, Genetic algorithm 1 Introduction The fabrication of sheet metal bending is widely used in automobile and aircraft industrial processes Needless to say; it is because a final sheet product of desired shape and appearance can be quickly and easily produced with relatively simple tool set. The production of high quality formed products in a short time and at a low cost is an ultimate goal in manufacturing. However, sheet metal forming may frequently produce the unacceptable products with wrinkle, tear, poor dimension precision, and so on, unless tool and process parameters are appropriately chosen. In particular, the dimension precision becomes a major concern in sheet metal bending process owing to the considerable elastic recovery during unloading which leads to spring-back. In fact there was some deviation in sheet metal bending between the component angle and tool angle after unloading because of springback, i.e. elastic deformation. Because of the existence of springback, the precision of products and subsequent assembly operations were severely affected. So how to effectively control springback

has been the key to precision forming and ultra-precision design of tools. The springback phenomenon is influenced by a combination of various process parameters, such as the tool shape and dimension, the sheet thickness, frictional contact condition, the material properties, and so on. The reliability and the stability of metal forming processes are usually low because of their dependence on many material and process parameters. As a result of this lack of robustness intelligent technologies have received much attention in a wide range of metal-forming applications in order to make a forming system with a large flexibility without the need of skilful experts, to achieve higher product accuracy and product quality. Developments in faster computation techniques have made intelligent techniques such as artificial neural networks (ANNs) a very popular choice in modelling of sophisticated phenomenon. ANN originated from the research on the biological brain. ANN models attempt to achieve good performance via dense interconnection of simple computational elements.

M. E. Golmakani, K. Kamali, M.-R. Akbarzade-T., M. Kadkhodayan, M. [email protected]



29-31 Aug 2007

، دانشگاه فردوسي مشهد1386 شهريور 7-9 ، هوشمندتمين كنفرانس سيستمهاي شه

29

Vehicle Type Recognition Using Probabilistic Constraint Support Vector Machine

Hadi Sadoghi Yazdi1, Sohrab Effati2

1-Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

2-Department of Mathematics, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

Abstract: The support vector machine (SVM) is one of the most powerful methods in the field of statistical learning theory for constructing a mathematical model in pattern classification. This paper presents a new support vector machine classifier for recognition of vehiche type which has been captured from traffic scene images. A new support vector machine classifier is presented with probabilistic constrains which presence probability of samples in each class is determined based on a distribution function. Noise is caused to found incorrect support vectors thereupon margin can not be maximized. In the proposed method, constraints boundaries and constraints occurrence have probability density functions which it helps for achieving maximum margin. Experimental results in the machine identification shows superiority of the probabilistic constraints support vector machine (PC-SVM) relative to standard SVM. Keywords: Pattern recognition, Vehicle type recognition, Machine identification, Support vector machine, Probabilistic constraints. 1. Introduction

Pattern recognition are widely used in various applications. In the pattern recognition usually there are two steps of processing associated. In the first step, pattern features are extracted in order to remove redundant information and emphasize only on the more important data. Second step include applying extracted suitable features to a classifier. In this stage, extracted features is categorized which tells the class that the target pattern belongs to. As there usually exist noises in the practical applications, it is important that the classification should have the capability of noise immune. The support vector machine (SVM) is a new classification technique in the field of statistical learning theory which has been applied with success in pattern recognition applications like signature verification [1], face detection [2], speech recognition [3], ECG beat recognition [4], star pattern recognition [5], hypertension diagnosis [6].

A lot of research has been done on intelligent transportation systems that from its results is the surveillance of road traffic based on machine vision techniques. Identifying the

offending drivers is examples of vision-based surveillance systems which for this purpose type of machine is necessary. Vehicle type recognition or machine identification includes two main stages: image segmentation and recognition. Segmentation is the first step in this procedure which objects are extracted using spatial and temporal methods [35, 36, and 37]. Edge, region, texture and color features are used in spatial segmentation and frame differencing and background subtraction are used in temporal segmentation. The optical flow method is a typical spatio-temporal segmentation. After detection of vehicles in the scene, a matching algorithm is used in the search area for finding similar vehicles in two consecutive frames. Finally, suitable features are extracted from segmented target (vehicle) for applying to classifier which this work proceed to it.

Such learning only aims at minimizing the classification error in the training phase, and it cannot guarantee the lowest error rate in the testing phase. In statistical learning theory, the support vector machine (SVM) has been developed for solving this bottleneck. Support vector machines (SVMs) as originally




29-31 Aug 2007

113

On-line Identification and Prediction of Lorenz's Chaotic System Using Chebyshev Neural Networks

Abstract: In this paper, a single layer functional link ANN based on Chebyshev polynomials is used for identification and prediction of chaotic systems. This model is linear in their parameters and nonlinear in the inputs. Therefore, on-line system identification is achievable by the use of recursive least squares method with forgetting factor. The remarkable prediction performance was gained using proposed Chebyshev neural network (CNN) model and recursive nonlinear predictor method on noise free chaotic Lorenz series. Keywords: Identification, Prediction, Chaotic Systems, Chebyshev Neural Networks. 1 Introduction A large set of methods has been developed recently which apply artificial neural networks (ANN) to the tasks of identification and prediction of nonlinear dynamic systems. Different neural network structures for nonlinear dynamic system modeling and identification is presented in [1]. The identification and prediction of nonlinear chaotic systems, which show "sensitive dependence on initial conditions" behavior, occupy an important place among of researcher interests. At present, most of the works on identification and prediction of nonlinear chaotic system using neural networks are based on multilayer perceptron (MLP) with backpropogation learning [2-4]. Identification and prediction of chaotic system using radial basis functions neural networks (RBFNN) are dealt in [5-7]. A comparative study on the effects of different basis functions used in the RBF neural networks for time series prediction purpose has been reported in [8]. Recently, there has been a considerable interest in the functional link artificial neural network (FLANN) [9-12]. In this paper we use a type of

FLANN based on Chebyshev polynomials to show that functional network architectures provide simpler and more efficient techniques to predict nonlinear time series. Because of single layer structure of CNN, its computational complexity is intensively less than MLP and can be used easily for on-line identification purposes [9, 12]. This paper is structured as follows. In Section 2 we give a brief introduction to Chebyshev neural networks. In this section, also we describe how CNN can be used for identification and prediction applications. Section 3 introduces Lorenz's system, while section 4 presents the simulation results of the multi-step ahead prediction on mentioned chaotic system using CNN. Section 5 gives some conclusions. 2 Chebyshev neural network (CNN) 2.1 Structure of CNN The CNN architecture used in this paper has a single layer structure, which introduced in [9]. CNN is a functional link network (FLN) based on Chebyshev polynomials. Among orthogonal polynomials, the Chebyshev polynomials occupy an important place, since, in the case of a broad class of functions, expansions in Chebyshev

A. Ashraf-Modarres V. Johari-Majd Tarbiat Modarres University Tarbiat Modarres University





29-31 Aug 2007

123

A Novel Hybrid Structure and Criteria in Modeling and Identification

* Emails:

A. Jajarmi: [email protected]. H. F. Marj: [email protected]. R. Shahnazi: [email protected]. N. Pariz: [email protected].

Abstract: In this paper, a hybrid structure based on combination of linear and fuzzy models is proposed. The proposed structure is a trade-off between goodness of fit and modeling simplicity. For evaluation of the hybrid model two criteria are also suggested which are compatible with both Akaike Information Criterion (AIC) and Schwarz-Rissanen Information Criterion (SRIC), respectively. The proposed criteria can also be used for evaluation of both linear and fuzzy models. The proposed hybrid structure is used to model a transformer’s current time series and results are compared with linear and fuzzy models by using suggested criteria. Comparison results indicate the effectiveness of the proposed hybrid structure. 1 Introduction

In past decades, the modeling and system identification are challenging and yet open problems. This is due to the fact that in modeling, it is necessary to find a good trade-off between keeping the model simple and minimizing the error between the model and the training data. However, keeping model simple conflicts with the other modeling objective, that is goodness of fit [8]. One of the main advantages of linear model is its simplicity and therefore fast convergence. Nonetheless due to the fact that most of real systems are nonlinear, utilizing linear models to identify these systems is not suitable, since the nonlinearity cannot be properly modeled and so the model loses accuracy. On the other hand, nonlinear models such as fuzzy models used for nonlinear systems have goodness of fit, but more complexity. Therefore, constructing simple and efficient model structure is a very important issue in nonlinear system identification. After a new model is constructed, it should be checked if it is

suitable or not. A good model is the one which minimizes the error between the model and the training data. On the other hand, a good model is the one which is as simple as possible. Therefore, a general criterion to check optimality trade-off between two conflicting modeling objectives (simplicity and goodness of fit) is necessary [1]. So, an identification criterion has two parts: one part is related to the error and the other is related to model complexity. One of the most important criteria for linear models is Akaike Information Criteria (AIC) which is suggested by Akaike in 1974 [1]. In 1978, Schwarz [2] and Rissanen [3], independently, derive a common criterion which is called SRIC. Other criteria that are similar to AIC have also been discussed in [4]-[7] where their difference is only in penalty coefficient for complexity selected as a function of sample size. In [8] AIC and SRIC are modified for evaluating fuzzy models construction. Certainly, the importance of simplicity and fitting the training data can be changed with respect to model application.

A. Jajarmi, H. F. Marj, R. Shahnazi and N. Pariz*

Electrical Engineering Department, Ferdowsi University of Mashhad, Mashhad, Iran




29-31 Aug 2007

141

Design of a VLSI Hamming Neural Network For arrhythmia classification

Abstract: The implantable cardioverter defibrillators (ICDs) detect and treat dangerous cardiac arrhythmia. This paper describes a VLSI neural network chip to be implemented using 0.35μ CMOS technology which acts as an intercardia tachycardia classification system. The Hamming net used to classify non binary input pattern and also reduce impact of noise, drift and offset inherent in analog application. Keywords: Implantable tachycardia arrhythmia classifier, Neural Network, Hamming Net. 1 Introduction In recently year, Artificial Neural Networks have been studied extensively and applied in medical field, and have been demonstrated to have much better pattern recognition ability. In this paper we present a neural network circuit used in a biomedical application, which is the implantable cardioverter defibrillator (ICDs). Implantable cardioverter defibrillator is a device which monitors the heart and delivers electrical shock therapy in the event of a life-threatening arrhythmia. At present most ICDs use only timing information from leads to classify rhythms [1].This means that they can not distinguish some dangerous rhythms from safe one, as in the case of ventricular-tachycardia arrhythmia. [2] Our chip is used to distinguish between two types of arrhythmia. The sinus tachycardia (ST) arrhythmia and the ventricular tachycardia (VT) arrhythmia, The ST is a safe arrhythmia occurs during vigorous exercises and is characterized with rate of 120beat/minute. The VT is a fatal arrhythmia with the same rate. They can be separated only by detecting the morphology changes in each one [2]. A typical waveform from an electrocardiogram (ECG) is shown in figure 1. It consists of several complexes, the P-complex, the QRS-complex, the T-complex and the U-complex [3].

Figure 1: A typical waveform of ECG

Most morphology changes appear in the QRS-complex. The QRS-complex for both the ST and VT arrhythmia’s are shown in figure 2. [2] Our studies indicate that; only two works are reported using Neural Network to detect such morphology changes [2][4].their Networks need to have training system and the weights of their Networks are off-chip learning.

Figure 2: Morphology change of QRS complex for both

ST & VT

Behzad Ghanavati Behbod Mashoufi [email protected] [email protected]

Microelectronics Research Center of Urmia University, Urmia, Iran




29-31 Aug 2007

177

Designing an optimal PID controller using Imperialist Competitive Algorithm

Esmaeil Atashpaz-Gargari & Caro Lucas [email protected] & [email protected]

Abstract— in this paper we use a new search heuristic called “Imperialist Competitive Algorithm” to design a optimal PID controller for a sample system. The PID controller is designed in such a way that it minimizes the sum of settling time, rise time, maximum overshoot and integral absolute error. A comparison among Imperialist Competitive Algorithm and Genetic Algorithm is made through designing the controller.

I.

I. INTRODUCTION roportional-integral-derivative controller (PID controller) is a generic control loop feedback

mechanism widely used in industrial control systems. A PID controller attempts to correct the error between a measured process variable and a desired set point by calculating and then outputting a corrective action that can adjust the process accordingly, based upon three parameters: proportional gain ( pK ), integral time constant

( iK ), and derivative time constant ( dK ). Traditionally, the problem has been handled by a trial and error approach. In the past decade more systematic methods have been introduced [1]. Ziegler-Nichols tuning formula is one of the best known tuning methods [2]. PID controllers are the subject to many researches in the area of control engineering and some other methods are proposed for tuning a PID controller [3] - [5].

Some papers use evolutionary methods to design a PID controller. [6] uses a multi objective genetic algorithm to tune a PID controller. In [7] a fuzzy-genetic approach is used for autotuning a PID controller.

This paper illustrates an application of Imperialist Competitive Algorithm (ICA) [8], by designing a PID controller for a given system such that the

output has the desired properties. At first In Section II, we briefly describe the Imperialist Competitive Algorithm. Then in Section III, we formulate the problem by introducing the PID controller and defining some of the most important characteristics of the system output. In section IV we apply a GA and ICA to the problem of designing a PID controller. Finally in Section V, we present our conclusions.

II. A BRIEF DESCRIPTION OF IMPERIALIST COMPETITIVE ALGORITHM

Imperialism is the policy of extending the power and rule of a government beyond its own boundaries. A country may attempt to dominate others by direct rule or by less obvious means such as a control of markets for goods or raw materials. The latter is often called neocolonialism [9]. Imperialist Competitive Algorithm (ICA) [8] is a novel global search heuristic that uses imperialism and imperialistic competition process as a source of inspiration. Figure 1 shows the pseudo code for this algorithm. Like other evolutionary ones, this algorithm starts with an initial population. In this algorithm any individual of the population is called a country. Some of the best countries in the population are selected to be the imperialist states and all the other countries form the colonies of these imperialists. All the colonies of initial population

P




29-31 Aug 2007

203

Fractional PID Controller Design based on Evolutionary Algorithms for Robust two-inertia Speed Control

Arman Kiani -B Naser Pariz [email protected] [email protected]

Department of Electrical Engineering

Ferdowsi, University of Mashhad, Mashhad, Iran Abstract: This paper deals with the speed control of two-inertia system by fractional order PI Dl m controller design with evolutionary algorithms. Fractional controller means the order of I, D controllers will not only be integer but also can be any real number. The significance of frictional order control is that it is a generalization and "interpolation" of the classical integer order control theory, which can achieve more adequate modeling and clear-cut design of robust control system. However, most of fractional order control researches were originated and concentrated on the control of chemical processes, while in motion control the research is still in a primitive stage. In this paper, we tune the controller parameters with EA to control of the two-inertia system, which is a basic control problem in motion control. The novelty of the proposed paper is using EA to tune the Fractional PI Dl m parameters and implementing this controller as a robust controller in comparison with classical PID. Keywords: Genetic Algorithm, Fitness function, Fractional Calculators, PI Dl d controller, PID controller.

1. Introduction Recently, several authors have considered mechanical systems described by fractional-order state equations [1], [2], [3], which mean equations involving so-called fractional derivatives and integrals (for the introduction to this theory see [4]). New fractional derivative-based models are more adequate than the previously used integer-order models. This has been demonstrated, for instance, by Caputo [7], [8], Friedrich [6] and [5]. Important fundamental physical considerations in favor of the use of fractional-derivative-based models were given in [8] and [1]. Fractional order derivatives and integrals provide a powerful instrument for the description of memory and hereditary effects in various substances, as well as for modeling dynamical processes in fractal (as defined by in [9]) media. This is the most significant advantage of the fractional-order models in comparison with integer-order models, in which, in fact, such effects or geometry are neglected.

However, because of the absence of appropriate mathematical methods, fractional-order dynamic systems were studied only marginally in the theory and practice of control systems. Works in [10], [11], [12], [13], and [14] must be mentioned, but the study in the time domain has been almost avoided. Fractional Order Control (FOC) means controlled systems and/or controllers described by fractional order differential equations. Expanding calculus to fractional orders is by no means new and actually had a firm and long standing theoretical foundation. The idea of using fractional-order controllers for the control of dynamic systems belongs to Oustaloup, who developed the so-called Commande Robuste d’Ordre Non Entier (CRONE) controller, which is described in his book [4] along with examples of applications in various fields (see also other references in [16]). In this paper some effective methods for the time domain design of fractional-order systems are presented. A concept of a PI_D_-controller, involving fractional-order integrator and fractional-order differentiator, is introduced. An example is provided to demonstrate the necessity of such controllers for the more




29-31 Aug 2007

217

Neural Networks for Fault Detection and Isolation of a Nonlinear Dynamic System

Roozbeh Razavi Far a , Hadi Davilu

a, Caro Lucas

b

a Department of Nuclear Engineering, Amirkabir University of Technology, Tehran, Iran. b Center of Excellence on Control and Intelligent Processing,

Department of Electrical and Computer Engineering, University of Tehran, Tehran, Iran.

E-mail Address: [email protected]

Abstract: The proper and timely fault detection and isolation of industrial plant is of premier importance to guarantee the safe and reliable operation of industrial plants. The paper presents application of a neural networks-based scheme for fault detection and isolation, for the pressurizer of a PWR nuclear power plant. The scheme is constituted by two components: residual generation and fault isolation. The first component generates residuals via the discrepancy between measurements coming from the plant and a nominal model. The neural network estimator is trained with healthy data collected from a full-scale simulator. For the second component detection thresholds are used to encode the residuals as bipolar vectors which represent fault patterns. These patterns are stored in an associative memory based on a recurrent neural network. The proposed fault diagnosis tool is evaluated on-line via a full-scale simulator to detect and isolate the main faults appearing in the pressurizer of a PWR.

Keywords: Neural Networks, Fault Detection and Isolation, Nonlinear Dynamic System, Pressurizer.

1. Introduction Fault diagnosis is usually performed by a three steps algorithm [1]. One or several signals are generated which reflect faults in the process behavior. These signals are called residuals. On the second step, the residuals are evaluated. A decision, regarding time and location of possible faults, is obtained from the residuals. Finally, the nature and the cause of the fault is analyzed by the relations between the symptoms and their possible causes. In order to describe the fault free behavior of the process under supervision, a mathematical model is employed; due to this fact, the term model-based fault diagnosis is used. Model-based approaches have dominated the fault diagnosis research for many years [2, 3].

The main disadvantage of this method is that, being based on a mathematical model; it can be very sensitive to modelling errors, parameter variations, noise and disturbances. The success of the model-based method is heavily dependent on the quality of the models; accurate modelling for a complex nonlinear system is very difficult to achieve in

practice. Different applications of fault diagnosis to industrial processes, which include conventional and artificial intelligence techniques are reported in [4]. However, for the second type of techniques, most of the power plant applications use a combination of analytical and/or computational intelligence tools [5]. Using adequate data base and methods for on-line and/or on-line training, neural networks are able to reproduce the dynamics of complex nonlinear systems; after training, they can estimate quite precisely the output of nonlinear systems [6, 7]. Employing measurements of the process under normal operation, if possible, or with the help of a realistic simulator, a suitable neural network can be trained to learn the process input-output behavior. The residuals generated using a neural network estimator can be evaluated via thresholds to obtain fault patterns. The fault pattern recognition can be done by means other neural network, which allows isolating different faults.

This paper presents a neural network scheme for fault diagnosis. It uses for residual generation an estimator, which consists of a bank of recurrent




29-31 Aug 2007

275

Semi-active Control of Structures Using Neuro-Inverse Model of MR Dampers

A. Khajekaramodin H. Haji-kazemi A. Rowhanimanesh M-R. Akbarzadeh Dept. of Civil Eng. Dept. of Civil Eng. Dept. of Electrical Eng Dept. of Electrical Eng Ferdowsi University Ferdowsi University Ferdowsi University Ferdowsi University a [email protected] [email protected] [email protected] [email protected] Abstract: A semi-active controller-based neural network for nonlinear benchmark structure equipped with a magnetorheological (MR) damper is presented and evaluated. An inverse neural network model (NIMR) is constructed to replicate the inverse dynamics of the MR damper. Linear quadratic Gaussian (LQG) controller is also designed to produce the optimal control force. The LQG controller and the NIMR models are linked to control the structure. The effectiveness of the NIMR is illustrated and verified using simulated response of a full-scale, nonlinear, seismically excited, 3-story benchmark building excited by several historical earthquake records. The semi-active system using the NIMR model is compared to the performance of an active and a clipped optimal control (COC) system, which are based on the same nominal controller as is used in the NIMR damper control algorithm. The results demonstrate that by using the NIMR model, the MR damper force can be commanded to follow closely the desirable optimal control force. The results also show that the control system is effective, and achieves better performance than active and COC system. Keywords: Structural Control, Semi-active, Neural Network, Nonlinear, MR Damper 1 Introduction The magnetorheological (MR) damper is generating a great interest among researchers in semi-active control of civil structures [1-6]. The MR damper is smart semi-active control device that generates force to a given velocity and applied voltage. The MR damper filled with a special fluid that includes very small polarizable particles that can change its viscosity rapidly from liquid to semi-solid and vice versa by adjusting the magnitude of the magnetic field produced by a coil wrapped around the piston head of the damper. The magnetic field can be tuned by varying the electrical current sent into the coil. When no current is supplied, the MR damper behaves similar to ordinary viscous damper, whereas its fluid starts to change to semi-solid as the current is gradually sent through the coil. Consequently, semi-active control using MR dampers are powerful devices that enjoy the advantages of passive devices with the benefits of active control. Additionally, they are inherently stable, reliable,

and relatively cost-effective; they require small activation power. One challenge in the use of semi-active technology is in developing nonlinear control algorithms that are appropriate for implementation in full-scale structures. Numerous control algorithms have been adopted for semi-active systems. These algorithms are either conventional methods based on mathematical formulation [1-6] or intelligent methods based on neural networks or fuzzy logic [7–12]. Interest in a new class of computational intelligence systems known as artificial neural networks (ANNs) has grown in the last few several years. This type of network has been found to be a powerful computational tool for organizing and correlating information in ways that have been proven to be useful for solving certain types of problems that are complex and poorly understood. The applications of ANNs to the area of structural control have grown rapidly through system identification, system inverse identification or controller replication [7-9].




29-31 Aug 2007

289

Evolutionary Constrained Design of Seismically Excited Buildings, Part I: Actuators Placement

Alireza Rowhanimanesh

Department of Electrical Engineering Ferdowsi University of Mashhad

[email protected]

Abbas Khajekaramodin Department of Civil Engineering Ferdowsi University of Mashhad

[email protected]

Mohammad-R. Akbarzadeh-T. Department of Electrical Engineering

Ferdowsi University of Mashhad [email protected]

Abstract: Optimal placement of actuators and sensors is an important problem in control of structures that is often selected without any systematic method. Appropriate placement strongly influences on the performance of control system. This study is presented in two parts In this paper as the first part, Actuators Placement is presented. In this way, a general method is suggested based on a proposed constrained genetic algorithm to determine the optimal placement of actuators in structures. The optimal placement scheme is general for passive, active and semi-active controls. It can handle linear and nonlinear constraints and it does not depend on strategy of control and dynamics of control system such as nonlinearities. The efficiency of proposed method is evaluated on the 20-story benchmark building. The optimal scheme is applied on the sample active LQG control system to place 25 and 5 actuators. The results show that the proposed method could find the optimal placement of actuators and improve the performance of control system. Generally, the proposed method is an approach to achieve the best utilization of available resources. Keywords: Earthquake, Structural Control, Structural Design, Actuators Placement, Constrained GA. 1. Introduction Civil structures might be excited by natural hazards such as earthquakes and strong winds. Since damages in some structures such as buildings and bridges might be dangerous for people and reconstruction of the damaged structures is very costly, designing a system that can protect and control structures against these dynamic loads is valuable. The first proactive researches on structural control were started by Yao in 1972 [1]. The initial methods are based on passive actuators such as dampers. Next, to reach higher levels of control, active control methods were proposed. In these methods, complex control algorithms can be programmed on a digital computer and suitable commands are sent to active actuators. The recent method is semi-active control that uses some actuators such as controllable dampers. This approach includes the advantages of both previous methods. A challenge that is common in all of these three methods is optimal placement of actuators and sensors that is often neglected and selected according to guess and experience without any systematic method. Appropriate placement strongly influences on the performance of control system. This problem is more necessary for actuators than sensors, because they’re more expensive, have limited capacities,

their installation is hard and only few numbers of them can be installed in each story. Thus, to achieve the best utilization, the optimal placement must be found before installation. In the following, some of the previous works are reviewed. Martin and Soong (1980) [2] considered the placement of active devices in structures for modal control. Lindberg and Longman (1984) [3] discussed the appropriate number and placement of devices based on modal control. Vander Velde and Carnignan (1984) [4] focused on structural failure modes to place the devices, and some other works performed by Ibidapo (1985) [5] and Cheng and Pantiledes (1988) [6]. Most of these methods are often problem specific. Takewaki (1997) [7] used a gradient-based approach to search for an optimal placement. Teng and Liu (1992) [8] and Xu and Teng (2002) [9] developed an incremental algorithm and Wu et al. (1997) [10] used both iterative and sequential approaches. Zhang and Soong (1992) [11] and Lopez and Soong (2002) [12] proposed sequential search methods for optimal damper placement. The main problem of these methods is converging to local optima. Simulated annealing as a guided random search was employed to place devices by Chen (1991) [13] and Liu (1997) [14]. Although these method could solve the problem of local optima, but they couldn’t always provide general and efficient




29-31 Aug 2007

297

Semantic Fuzzy Image Segmentation Using Human Interaction

Hadi Sadoghi Yazdi, Seyed Ebrahim Hosseini Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

E-mail: [email protected]

Abstract

The aim of this paper is presentation of a new fuzzy image segmentation algorithm. In the proposed algorithm, human knowledge is used in clustering features for fuzzy image segmentation. In fuzzy clustering, the membership values of extracted features for each pixel at each cluster change proportional to zonal mean of membership values and gradient mean of adjacent pixels. The direction of membership variations are specified using human interaction. The proposed segmentation approach is applied for segmentation of texture and documentation images. Results show that the human interaction eventuates to clarification of texture and reduction of noise in segmented images.

1. Introduction

Image segmentation is not done as well without consideration of semantic respects [1]-[2]. The human brain uses methods which has semantic respects in image segmentation to receive specific aims. Albeit researchers have presented numerous segmentation approaches [3] but image segmentation by a human being is completed intelligently so that different mathematical approaches and or learning based methods can not present suitable effective method [2], [4].

Image segmentation based on recognition [4], [5] tries to use recognition of objects in the scene. As a result, segmentation is performed perfectly, but applied recognition systems in these methods utilize low level features such as color, texture and edges therefore, can not be accept as semantic segmentation approachs.

Although, one aim in image segmentation in various applications is automation, but because of need of wide initial knowledge or an expert system like human, segmentation can not be completed unless with human interaction. Fig 1 shows this interaction.

Fig. 1: Interactive image segmentation system

A few researches have been accomplished to image

segmentation by Human Computer Interaction (HCI) which can be categorized in three groups,

a) Using suitable interaction equipments for interactive image segmentation in which segmentation is performed by high-performance hardware for better usage of human mind, like three dimensional mice [6]. b) Manual segmentation using professional operator in medical image segmentation [7]-[9] and map recognition [10]. c) Manual initialization in image segmentation algorithms, for example applying initial value in 3D image segmentation to deformable surfaces [11].

In this paper a novel human interaction image segmentation algorithm is presented which have manifest features as follows, • Increasing the performance of image

segmentation algorithms by increasing suitable controllable parameters. • Prediction of parameters using human

interaction. Figure (2) shows configuration of the proposed

interactive fuzzy image segmentation.

Fig.2: structure of the proposed interactive fuzzy

image segmentation system




29-31 Aug 2007

375

Improving Power System Stability by Designing Supplementary Controller of HVDC Using Real Genetic Algorithm

Abstract: This paper investigates the ability of Real Genetic Algorithm (RGA) in designing supplementary controller of High Voltage Direct Current (HVDC) link to damp the power system oscillation. A conventional lead-lag structure is considered for the supplementary controller. The aim of the proposed control strategy is to choose the best controller parameters in such a way that the dominant eigenvalues of the closed-loop system are shifted to the left-hand side of s-plane as far as possible. Also, the binary version of genetic algorithm (BGA) is used to design a supplementary controller for HVDC. The characteristic convergence and time simulation results show that both versions of GA have good capability in solving the problem but RGA gives better results.

Keywords: Real genetic algorithm, binary genetic algorithm, power system stability, dynamic stability, HVDC. 1 Introduction HVDC links has been widely applied in power transmission for a number of years and have provided utilities around the world with important technical solutions to a wide range of transmission needs due to their excellent and flexible control ability. Direct Current transmission can be between independent systems or between points within a system. By DC link power flow can be controlled precisely and very rapidly. By controlling its power transfer, the DC link can help the system operator to dictate the power flows in the adjacent ac lines. Also, by rapidly changing its power transfer, it can improve ac system stability. It can damp out post-disturbance swings. It can act as a voltage regulator by switching its reactive power banks or by

adjusting control angles to absorb more or less reactive power. Therefore, HVDC links can be effectively used for damping electromechanical oscillations, stabilizing power swings, reducing the life-fatigue effects of Sub-Synchronous Resonance (SSR), etc. The development of Voltage Source Converter (VSC) technology (used for instance in HVDC Light interconnections) can improve also the network voltage compensation and the transmission grid load-ability, reducing the risks of voltage instability and collapse [1-7]. Since, their contributions to the damping of system oscillations are of great importance for achieving satisfactory system performance, in this paper a supplementary controller is designed for a HVDC link. Despite the potential of modern control techniques, intelligent control is used to design a conventional lead-lag structure. BGA is used to design supplementary controller of HVDC in [8-10].

Saeid Haidari, Malihe M. Farsangi and Hossein Nezamabadi-pour Electrical Engineering Department of Shahid Bahonar University, Kerman





29-31 Aug 2007

381

A Soft Computing Approach in MAS Modeling

Ehsan Rafiee1, Morteza Analoui1,Bardia Aghabeigi1, Seyyed Mohammad Saeed Tabatabaee1,Mohammad Jafar Abdi1

Computer Engineering Department, Iran University of Science and Technology { E.Rafiee, Analoui, B.Aghabeigi, S.Tabatabaee, M.Jafarabdi }@gmail.com

Abstract. Nowadays multi-agent modeling is one of the important problems in problem-domains in which several agents are involved. One of the main reasons for modeling agents is to become capable of predicting their behaviors in special situations. In this paper a modeling algorithm for multi-agent systems is presented which is applicable in domains like RoboCup coach competitions. (a very chaotic and uncertain domain with large number of agents).This algorithm is a combination of a classic data mining algorithm named association rule mining and fuzzy set theory which leads to a soft computing approach. Also some evaluation methods for recognition of models are presented and finally, some experiments for measuring accuracy of models and evaluation methods are outlined.

Keywords: MAS; Fuzzy Logic; Association Rule Mining; Opponent Modeling, RoboCup

Multi agent systems have found many applications in so many different areas and bring out many interesting challenges. Multi agent modeling is one of major challenges that its main goal is prediction of opponents’ behaviors. This leads to a new branch of modeling problems, thus a lot of research on opponent-modeling over plan recognition and domain-dependent operator hierarchies is done. Yet, most approaches cannot be applied in dynamic, non-discrete and uncertain multi-agent-systems.

In soccer coach simulation league, coach is one autonomous agent providing advice to other autonomous agents about how to act. This advice is in format of standard coach language called Clang. The problem of creating agents, is the problem of designing intelligent systems to control and observe multiple robots and provide the robots with the suitable advice to enhance their performance.

The online coach within the simulation league has become more powerful over the last few years. Therefore, new options with regard to the recognition of the opponent’s strategy are possible. For example, the online coach is the only player who gets the information of all the objects on the field. This leads to the idea for determining the opponents play system by the online coach and then choose an effective counter-strategy.

In recent years the coach competition structure has been changed in a way which tries to more concentrate on opponent modeling and counters strategy design. This task specially is divided into three subtasks: extracting game patterns from some log file which can be processed offline, designing some counter strategies which can be used to make the patterns occur, and developing a recognition engine which observes the game and announces the recognized patterns.

In this paper a data mining approach is presented for discovering opponent behaviors. Discovered behaviors are represented in the form of a rule-based model.

Several unsupervised mining algorithms such as association rule mining have been presented for mining rule-based models so far. In this paper a classic algorithm of association rule mining called Apriori-Tid has been chosen as a base algorithm for mining every possible rule in opponent behaviors. In domains such as coach simulation there are some attributes that impose some extra complexity to rule mining problems. For example continuous variables that constitute opponent behaviors stand as a problem named quantitative variables. Standard algorithms for extracting association rules use several discretization methods in preprocessing phase to overcome this problem but these discretization leads to problems such as sharp boundaries and data loss. In this paper a combined approach of Apriori-Tid and fuzzy logic has been presented for overcoming




29-31 Aug 2007

407

An Evolutionary Control Model for a Generic Multiagent System Using Artificial Immune Systems

Abstract: In this paper we propose a method for controlling the behaviour of agents in a multiagent environment. We demonstrate here that functionalities of the biological immune systems are apt to apply in multiagent systems. The AIS-based multiagent system consists of a set of exploring agents in the workspace to find a task. When agents see a task they bid to do it, wining of bidders is based on the ability of them to do the task. The one with a higher ability will gain on the task. After achieving a task, the agent matures itself as a result of competence, avoiding the other agents to grab the task. Agent also requests help when even after maturation is not able to do the task entirely by its own. Through this mechanism, a self-organized, distributed system with complete interactions between components is achieved. Experimental results are presented, proving the efficiency of the overall system. Keywords: Multi agent system, Artificial Immune System. 1 Introduction Natural Immune System is a complex system consisting of collection of autonomous agents. No central control exists in immune system, but the components work successfully as a whole. The agents communicate with each others and complete each other’s operations. So immune system is a self-organized fully distributed system, capable of memory management, self-organization, and adaptive control. It also has properties such as specificity and diversity [1]. These properties of natural immune system are of great interest in adapting immune system paradigm to various engineering systems. This adopted engineering analogue is called Artificial Immune System (AIS). AIS has been studied widely in the fields of Artificial Intelligence (AI) due to its deep inspiration to the engineering sciences. The essences of human im-mune system properties are imitated to perform complicated tasks, for example, learning strategies, adaptive control, memory managements and self-organization. One of these engineering systems that immune system

adapts to, is multiagent sys-tem. We can apply control mechanism and communication strategy of immune system to multiagent systems. The multiagent system we proposed in this paper, address how agents with differ-ent capabilities achieve continuously emerging tasks in a dynamic environment through communication and strategic control. For delineation the behavioral strate-gies and rules that govern our system we define a formal model. Besides, a coopera-tion model is presented in this paper. In natural immune system one of the most important properties is to be adaptive. When an unfamiliar antigen enters the body, even if there is no specific antibody for that antigen, the immune system tries to create one which is able to annihilate it, so one of the significant parts of our system is maturation of agents to successfully handling the tasks. Through capability maturation, Artificial Immune System (AIS) agents are able to accomplish the tasks more skilled. The other property of our pro-posed system is that it imitates the immune memory, not exactly, but to help the system to make more powerful responses to already seen tasks.

B. H. Helmi, A. T. Rahmani, N. Helmi*

Department of Computer Science and Engineering, Iran University of Science and Technology, Narmak,

Tehran, 1684613114, Iran, *Department of Computer Engineering,

Islamic Azad University of mashhad, [email protected], [email protected], [email protected]



29-31 Aug 2007


417

A Match Making Method in a Multi-Agent Bilateral Market

Hamed Kebriaei M.Sc. Student

Tarbiat Modares University [email protected]

Vahid Johari Majd

Associate Professor Tarbiat Modares University

[email protected]

Ashkan Rahimi-Kian Assistant Professor

University of Tehran [email protected]

Abstract: In this paper, an agent matching architecture for bilateral contracts of a multi agent market is proposed. The bilateral market contains a number of sellers and buyers who face opponents for negotiation and signing bilateral contracts. Each agent has a hierarchical representation of trading commodity attributes, where based on that it will create a tree structure of attributes. Using this structure, we apply a modified version of fuzzy similarity algorithm to compute similarity between each pair of buyer and seller agents' trees. Then, we use game theory and the concept of Stackelberg equilibrium to assess the matchmaking among the seller and buyer agents. Agents who lose contract or want to sign a new contract have a chance to restart the procedure. Keywords: Multi agent, market, fuzzy similarity, game theory. 1. Introduction

In today's world with rapid developments of internet, electronic commerce is growing fast. Now, we can have multi-agent systems with software agents as brokers, sellers and buyers that can negotiate and sign bilateral contracts for us. Usually the interactions among agents in a multi-agent market are complex.

Agents are typically interested in multi-attribute commodities with interdependency among the attributes. The interdependency of these attributes is considered in several research works in different ways. Some assumed nonlinear utility functions for the agent [9, 12], and several papers used the hierarchical model for multi attribute goods such as the tree representation model [1, 11].

An agent normally specifies a desirable range of services (or products) it needs instead of specifying them with crisp values. This is because specifying the amounts of services in crisp values may cause profit loss for the agent. Therefore, a fuzzy representation of supply or demand for products/services seems to be a reasonable approach [7, 8].

The Agent's objective and market supply and demand are essential factors for decision making in multi-agent markets, and simultaneous decision making leads to competition among agents. Thus, an Agent decision directly affects the objectives of other agents and their decisions. Therefore the issue of coordination in such an environment seems to be a necessary task. Game theory can be used to manage this conflict [10,14].

In this paper, we present a model for matchmaking among sellers and buyers in a bilateral market. This approach helps agents, in presence of decisions confliction; they make most possible beneficial decision and facilitate bilateral contracts.

This paper is organized as follows: In section 2, some preliminary backgrounds on weighted tree similarity algorithm and fuzzy similarity measures is discussed. In section 3, the proposed agent matching architecture is presented. This section includes the new fuzzy similarity measure and game theoretical approach for matchmaking among agents.

2. Preliminary Background

2-1. Tree Similarity Algorithm



29-31 Aug 2007


423

Optimized Elastic Bunch Graph Matching using Genetic Algorithm for Face Recognition

Abstract: In this paper a new method for optimization of Elastic Bunch Graph Matching (EBGM) algorithm in frontal face recognition is presented. In EBGM algorithm, some pre-determined wavelength of Gabor wavelet is used to extract features from face image. For optimization of EBGM algorithm, Genetic Algorithm (GA) is used to select the best wavelengths of Gabor wavelet. For evaluation, algorithm has been tested on 300 classes of FERET face database. In training phase, only one image per class is trained. The recognition rate of optimized EBGM is about 91%. Also the optimized EBGM can run 1.5 times faster than original EBGM. Keywords: Elastic Bunch Graph Matching (EBGM), Face Recognition, Gabor Wavelet, Genetic Algorithm. 1 Introduction Facial image is the most common biometric characteristic used by humans to make a personal recognition, hence the idea to use this biometric in technology. Face identification involves extracting a feature set from a two-dimensional image of the face image and matching it with the templates stored in a database. This is a non intrusive method [1]. The applications of face recognition range from static (mug shots) to dynamic, uncontrolled face identification in a cluttered background (subway and airport). More applications of face recognition and its commercial products are discussed in [2]. Face recognition methods are divided to three categories: template based, feature based and hybrid method. Template based approaches such as Principal Component Analysis (PCA) and Independent Component Analysis (ICA), use template matching methods and use the whole face region as the raw input of recognition system to find the best matching. In other hand, feature based approaches such as EBGM, extract some local features from face image and compare features of facial images for recognition. Hybrid method such as human perception system, uses both template based and feature based approaches to recognize

facial images. One can argue that this method could potentially offer the better of the two types of methods [1,2]. 2 Related Works Face recognition is an old challenging problem in pattern recognition research. Many of researchers focus his/her researches on this branch. Face recognition had been investigated from early 1970s to now. In this section, only some last researches about Elastic Bunch Graph Matching algorithm have been investigated. First time, Wiskott et al [3] introduced Elastic Bunch Graph Matching (EBGM) algorithm for face recognition in 1997. In EBGM algorithm, faces are represented by graphs, which used Gabor wavelet transform for extracting features in each node of graph. The node of graphs has been named landmark and the Gabor coefficients of landmarks have been named as jet. In recognition phase, the algorithm recognizes novel faces by first localizing a set of landmark features using bunch graph model and then measuring similarity between these features. Wiskott et al [4] compared EBGM algorithm with other high recognition rate algorithms on FERET

Mohamd Hoseyn Sigari, Adel Torkaman Rahmani Computer Engineering Department of Iran University of Science and Technology

[email protected]



29-31 Aug 2007


441

A NEW AND ROBUST APPLE EVALUATION METHOD USING IMAGE PROCESSING

Abstract: Fruit evaluation is a necessary component of vegetable and fruit sorting system. Recently, machine vision applications for sorting and inspecting some fruit vegetables have been studied by many scientists. In this paper a new and robust computer vision based system for apple evaluation using image processing is presented to automatically grade apples. The process of segmentation of apples is performed by applying a threshold and a few morphological operations such as opening and closing. Next each apple gets a label using run-length algorithm. Now calculating the measure properties of the apple can be done easily. The next step is detecting the apple skin bruises and the defected areas of apple skin that can be done performing tophat operation on the image. By comparing the results of our approach with the standard apples we can clearly see that our approach will produce good results for sorting the apples. Keywords: Apples, color, image processing, machine vision. 1 Introduction Computer vision is a young technology starting from 1960s [1]. From 1970s it began to grow in both theory and application rapidly. It is reported that more than 1000 papers are published each year in various fields of this technology like medical diagnostic, automatic manufacturing, robot guidance, remote sensing and etc [2]. The main core of machine vision systems is image processing and image analysis with numerous methods to achieve various properties. Recently the usage of computer vision is growing rapidly in many applications to substitute visual senses of human [3], [4], [5], [6], [7]. Traditionally evaluation of food products is performed by humans. These manual operations are time consuming. Moreover the accuracy of this operation cannot be guaranteed [8]. For example a human must grade at least 20 apples in a second that can produce lots of errors and it relates to subjective factors. During the last decade scientists have studied on several methods for automatic evaluating the quality of food products and fruits [9] and numerous works in this category have been reported [10].

Nowadays, because of the advances in electronic technology, machine vision technology can be applied to the development of an automatic fruit evaluator. Machine vision enables to handle a large amount of raw data and perform remote judgment. Computer vision based food evaluation is a hard but necessary task for increasing the speed of sorting food products and reducing human errors in this process. This technology can provide a reliable judgment system independently from human subjective factors. In Japan fruit vegetables are generally sorted into grades based on size or weight before marketing[11]. But these properties are not the only factors which can be used to describe the quality of fruits. Among them the shape and color are extremely important but unfortunately these properties are mostly neglected and grade sorting based on shape, damage and color (for example in the case of orange, apple, and cucumber) is still in the initial stage and in most cases performed manually. This paper presents a new and robust grade judgment system with a high performance rate using image processing technology. The simplicity

H. Mirzaei, M. Saraee Electrical and computer engineering department, Isfahan University of technology




29-31 Aug 2007


465

AUTOMATIC QUALITY CONTROL OF FRIED POTATO USING MACHINE VISION

Ehsan Lotfi, Hosein Mirzaee

[email protected] Islamic Azad University of Mashhad , Iran.

Khorasan Research Center for Technology Development, Mashhad, Iran.

Abstract: Frying of potatoes causes some changes in their microstructures. By studying these changes we have presented quite suitable features for automatic analysis of microscopic images taken from fried potatoes, and have also introduced a new mechanism based on machine vision for automatic quality control of fried potatoes. Experimental results show that the presented structure may well be used for controlling the quality of related products. Keywords: Neural networks, Machine Vision, Texture recognition, Quality control, Potato microstructures. 1 INTRODUCTION One of the methods for preparing food is frying. This method is widely used throughout the world and nearly everywhere such fried food is controlled in terms of quality and health. One food material that has attracted numerous studies to its frying in the past is potato. Our goal here is to let the analysis and qualitative control of fried potato be done algorithmically; or in other words, automatically and by a machine. To that purpose we shall first review the works of the past in order to extract suitable features for machine vision. In [1] there is an analysis of the microstructures of potatoes while being fried. In this paper it has been shown that by increasing temperature from 20°C to 150°C the potato cells change their shapes and their circularity decreases. Also, the starch granules inside the cells swell and gelatinize, and expand to whole volume. In this paper it has been shown that after gelatinization, the starch of the cells get dehydrated and then shrink. In [2] and [1] it has been expressed that studying the frying of potato cells clearly shows that the starch granules constantly swell and expand throughout the cell in a certain temperature (e.g. 60°C to 70°C) by the intercellular water. In [3] it has been said that after this phase, steam bubbles crack and pass through the pores in the cell walls and find their way into the oil interface. In [4] it has been shown that before being dehydrated in higher temperatures, the swollen starch granules remain like a compact mass pressed on the outer

cell walls. In [3] the rate of penetration of oil in the potato during frying has been estimated by the changes in the tissue surface and X-ray photography. There are many more papers that have worked on fat uptake, e.g. [8], [5], and [6]. And some works on quality control of fried potatoes used classification methods and neural network such as [10], [11]. In [10] there is an approach to classify the potato chips using pattern recognition from digital color macroscopic images. In [9], analysis of digital color macroscopic images of fried potato chips were combined with parallel LC-MS based analysis of acrylamide in order to develop a rapid tool for the estimation of acrylamide during processing. [11] that uses image analysis and artificial neural network for quality control of potatoes in chips industry and [12] that includes texture analysis of fried potato. According to what was said above, we rewrite the process of microscopic changes in potatoes during frying: (1) raw potato cell, (2) swelling of starch granules inside the cell, (3) gelatinization of swollen starch granules, and (4) shrinkage of potato cells. The algorithm we have presented enables the machine to automatically determine and figure out in which state the potato microstructures are, and whether or not the fried potato is in its best form in terms of quality. The overall structure of the paper is such that we first describe the proposed structure for separating the tissues and inferring the results, then we point out to the equipment being used and finally explain the results of implementation and assessment of the algorithms.




29-31 Aug 2007

471

A Wavelet-Based Neuro-Fuzzy System for DGPS Corrections Approximation

M. R. Mosavi

Department of Electrical and Computer Engineering, Behshahr University of Science and Technology, Behshahr, 48518-78413, Iran E-mail: [email protected]

Abstract: When Global Positioning System (GPS) measurements are made by two users within the same GPS satellite transmission sight, the associated errors are mainly similar. Consequently, knowing the exact location of the receiver with respect to GPS satellites within view allows the measurements errors to be estimated. Thus, these error estimates may be extracted by other nearby GPS users if relayed properly. This correction scheme is the idea behind Differential GPS (DGPS). Inspired by the theory of Multiresolution Analysis (MRA) of wavelet transforms and fuzzy concepts, a Fuzzy Wavelet Network (FWN) is proposed for approximating DGPS corrections. The FWN combines the traditional Takagi-Sugeno-Kang (TSK) fuzzy model and the Wavelet Neural Network (WNN). Each fuzzy rule corresponding to a WNN consists of single-scaling wavelets. The non-orthogonal and compactly supported functions as WNN bases are adopted. The online structure/parameter learning algorithm is performed concurrently in the FWN. The tests results on the collected real data are given to illustrate the performance and effectiveness of the proposed model. The results emphasize that RMS error reduces to less than 0.7m. Also, it is shown that performance FWN is better than single WNN. Keywords: Fuzzy Wavelet Network, Wavelet Neural Network, DGPS, Corrections, Approximation 1 Introduction GPS is an operational constellation consisting of 24 satellites orbiting the earth every 12 hours, and acting as reference points from which receivers on earth triangulate their positions. The GPS has made navigation systems practical for a number of land-vehicle navigation applications. Today, GPS-based navigation systems can be found in motor vehicles, farming and mining equipment, and a variety of other land-based vehicles (e.g., golf carts and mobile robots) [1]. Inaccuracies in the GPS signal can come from a variety of sources: satellite clocks, imperfect satellite orbits, the receiver errors, and the signal's trip through the earth's atmosphere. One efficient way to reduce sources of error is by differentiation. Differential corrections are obtained by comparing the base station "true" location with the estimated location. Consequently, the errors associated with each

satellite pseudorange are computed. These estimated errors are used to correct the rover position, hence, improving its accuracy [2]. Recently, wavelets have become a very active subject in research area. Especially, WNNs inspired by both the feedforward networks and wavelet decompositions have become a popular tool for function approximation. For the WNN with fixed wavelets, the main problem is the selection of wavelet bases/frames. The wavelet bases have to be selected appropriately since the choice of the wavelet basis can be critical to approximation performance. For WNN with variable wavelet basis, a new approach has first been presented by initializing the WNN as truncated wavelet frames, then follows by training with a Back Propagation (BP) algorithm. Also, the traditional AutoRegressive (AR) external input model is incorporated with WNN introduced by

Intelligent Systems Scientific Society of IranIntelligent Systems Scientific Society of Iran Intelligent Systems Scientific Society of IranIntelligent Systems Scientific Society of Iran


29-31 Aug 2007


487

Creating New Color Space Using Convex Constraint Programming Applied to Skin Color Detection

Hadi Sadoghi Yazdi Seyyed Meysam Hosseini Seyyed ebrahim hosseini

Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran

Abstract: Each three-component collection such as {Red, Green, Blue} (RGB), and {Luminance Y, Chrominance Cr, Chrominance Cb} (YCbCr) is termed as a color space. Many color spaces are related to each other by linear transformations that are captured by 3×3 matrices. Hence a given color, and thereby any color image, can be represented in terms of another color space by transforming its 3-d vector representation using the 3 × 3 matrix. The Main target of this paper is introduce new color transform from viewpoint of convex constraint programming. Skin detection is used as benchmark problem for the proposed algorithm. In the New color space, the skin and non-skin classes are separated as well. This problem is converted to a convex constraint programming which Lagrange multipliers method is used for solving this problem. Founded converting matrix is tested in skin detection in simple to complex scene. Obtained results over many databases are compared with existing methods which show superiority of the proposed method. Skin and non-skin clusters in the new space color have clustering criteria better than RGB and YCbCr color space. Keywords: Color space; Convex constraint programming; Skin detection; Clustering criteria; Lagrange multipliers. 1. Introduction

Color is a 3-dimensional psychophysical phenomenon and is represented in color space models whereby individual colors are specified by points in these spaces. R, G, B primaries can produce a gamut of (28)3 different colors [1]. RGB is the color space usually used in digital images. Each pixels use 8 bits for each one of its color components (R, G and B), in a total of 24 bits for pixel. The color space converter transforms the color information form the RGB space to the other spaces as YCbCr space and it should maintain the representation of each one of the new space components with the same amount of bits used to represent each component of the input space (R, G and B). The calculations performed in the color space conversion from RGB to YCbCr are presented below. Parcels of each R, G and B input components are considered in the calculation of the output components in the space YCbCr [2].

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

−−−−=

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

BGR

CrCbY

081.0419.05.05.0331.0169.0

114.0578.0299.0

(1)

CIE standardized color order systems by specifying the light source, the observer and the methodology used to derive the values for describing a color. The XYZ color system is also accepted then and it has been used ever since. In this system, Y represents the brightness (or luminance) of the color, while X and Z are virtual (or not physically realizable) components of the primary spectra [3].

Many color spaces are presented but other viewpoint is theories of color vision which are derived from the sums and differences of the three cone types. One mechanism (often referred to as the ‘‘luminance’’ mechanism) signals a weighted sum of long-wavelength-selective (L) and medium-wavelength-selective (M) cones, i.e., ‘‘L+M’’ (with some debate regarding the contribution of short wavelength selective (S) cones: [4, 5, and 7]. Two chromatic mechanisms signal weighted sums and differences of the cones. The ‘‘L-M’’ mechanism signals differences between L- and M-cones (and is often referred to as the ‘‘red/green’’ mechanism). The ‘‘S-(L+M)’’ mechanism signals differences between S-cones and the sum of L- and M-cones (and is often referred to as the ‘‘blue/yellow’’ mechanism).




29-31 Aug 2007

515

Fuzzy Path Planning in a Plane With Fixed Obstacles

M. Zamirian ∗,a , A.V. Kamyad b

a Department of Mathematics Islamic Azad University of Bojnourd, Iran b Department of Mathematics Ferdowsi University of Mashhad,Mashhad 91775-1159, Iran

Abstract: In this paper a new approach for finding optimal path planning in a plane with fixed obstacles is discussed. We consider a movable rigid body in a plane with fixed obstacles. The goal is to find the optimal path which brings rigid body from a given initial point to a given final point such that the length of path is minimum and the distance between rigid body and obstacles is maximum. By considering the length of path and the distance between rigid body and obstacles as objective functions, we obtain a multi-objective problem. Because of the imprecise nature of decision maker's judgment, these multiple objectives are viewed as fuzzy objectives. Then we determine intervals for the optimal value of objective functions such that these intervals for the distance between rigid body and obstacles are given and for the length of path is achieved by solving two optimal non-linear programming problems (ONPP). Now, we define a strictly monotonic decreasing or increasing membership function as degree of satisfaction for any objective functions on achieved intervals. Then the optimal policy is to find an optimal path which maximize all of membership functions, simultaneously. Thus, we obtain an ONPP which gives a (local) Pareto solution for original goal. Numerical example is also given. Keywords: Optimal path planning; Multi-objective; Membership function; Pareto optimal. 1. introduction The problem of finding an optimal path planning for a movable rigid body in a plane with fixed obstacles is one of the most applicable problems, especially in robot industrial and recently surgery planning and etc. Latombe [1] has gathered novel methods for path planning in the present of obstacles and some extensions of them. In reference [2] two novel approaches, constrained optimization and semi-infinite constrained optimization, for unmanned under water vehicle are considered. In reference [3] is presented a new

* Corresponding author E-mail address: [email protected]

approach based on measure theory for finding approximation optimal path planning problem in the present of obstacles. In all of above references the distance between rigid body and obstacles are assumed crisp values. But, in practice we desire to achieve the shortest path with the greatest distance between rigid body and obstacles, simultaneously. All of these objectives are contradictory such that the optimization of one objective implies the sacrifice of other target. Then we need a multi-objective decision making technique to look for a satisfying solution from these conflict objectives. Optimization for a multi-objective problem is a procedure looking for a compromise policy. The result, called a Pareto optimal that consists of an infinite number of alternatives. In references [4,5] there are many methods according to different criteria. For example, Cohon [5] categorized two methods generating and preference-base. The



29-31 Aug 2007


631

Improvement of STATCOM Performance with Optimum LQR and Pole placement Controller Based on Genetic Algorithm

S.Eshtehardiha - Gh.Shahgholian

Department of Electrical Engineering, Islamic Azad University, Najafabad Branch, Esfahan, Iran Fax: +98331 2649936 Email: [email protected]

Abstract: Static Synchronous Compensator (STATCOM) is a device capable of solving the power quality problems at the power system. These problems happen in milliseconds and because of the time limitation; it requires the STATCOM that has continuous reactive power control with fast response. In this paper, a LQR (Linear Quadratic Regulator) and Pole placement method for STATCOM control is introduced. The former controller designing needs to positive definite matrix selection and the later is relative to desired pole places in complex coordinate. In this article, matrixes coefficients and dominant poles of closed loop transfer function are selected based on Genetic algorithm method. These methods are tested in MATLAB, and their results are obtained. Keywords: STATCOM, Genetic algorithm, LQR controller, Pole placement. 1 Introduction Stability enhancement is of great importance in power system design. As we all known, generator excitation control plays an important role in stability enhancement of power systems. Generator excitation controllers are helpful in achieving rotor angle stability or voltage regulation enhancement [1]. With only excitation control, the system stability may not be maintained if a large fault occurs close to the generator terminal, or simultaneous transient stability and voltage regulation enhancement may be difficult to achieve. With the development of power electronics technologies, several Flexible AC Transmission System (FACTS) devices [2] at present or in the further can be used to increase the power transfer capability of transmission networks and enhance the stability of the power system. The STATCOM is normally designed to provide fast voltage control and to enhance damping of inter-area oscillations. A typical method to meet these requirements is to superimpose a supplementary damping controller upon the automatic voltage control loop [3]. Several recent articles have reported that STATCOM can provide damping to a power system [4]-[8]. They have also been shown to improve torsional oscillations in a power system [9].The three-phase STATCOM differs from other reactive power supply devices as well, such as

fixed capacitors [10]-[12]. The mechanically switched capacitors and Static Var Compensator (SVC) which include actual energy storage elements such as capacitors or inductors, in that the ability for energy storage is not a strict requirement but is only necessary for system unbalance or harmonic absorption. So it is an ideal three-phase reactive power source supplies (or absorbs) exactly zero real power on an instantaneous basis. Two basic controls are implemented in a STATCOM. The first is the a.c. voltage regulation of the power system, which is realized by controlling the reactive power interchange between the STATCOM and the power system. The other is the control of the d.c. voltage across the capacitor, through which the active power injection from the STATCOM to the power system is controlled [13]. PI controllers have been found to provide stabilizing controls when the a.c. and d.c. regulators were designed independently. However, joint operations of the two have been reported to lead to system instability because of the interaction of the two controllers [13,14].The STATCOM AC and DC voltage controllers can be the proportional plus integral (PI) controllers [13].The modelling and control design are usually carried in the standard synchronous d–q frame[15]. Although, the cascade control structure yields good performance, it is not very much effective for all operating conditions because of the unsuitability of



29-31 Aug 2007


637

Multi-objective VAr Planning with STATCOM Using Immune Algorithm

Abstract: In this paper, the ability of Immune Algorithm (IA) is investigated for VAr planning with the STATic synchronous COMpensators (STATCOM) in a large-scale power system. To enhance voltage stability, the planning problem is formulated as a multi-objective optimization problem for maximizing fuzzy performance indices. The multi-objective VAr planning problem is solved by the fuzzy IA and the results are compared with those obtained by the fuzzy Genetic Algorithm (GA). Keywords: Immune algorithm, genetic algorithm, STATCOM, multi-objective optimization, fuzzy performance indices. 1 Introduction Voltage collapse and other instability problems can be related to the system’s inability to meet VAr demands [1]. Efforts have been made to find the ways to assure the security of the system in terms of voltage stability. Flexible AC transmission system (FACTS) devices are good choice to improve the voltage profile in a power system, which operates near the steady-state stability limit and may result in voltage instability. Taking advantages of the FACTS devices depends greatly on how these devices are placed in the power system, namely on their location and size.

Over the last decades there has been a growing interest in algorithms inspired from the observation of natural phenomena [2-8]. The ability of different algorithms is investigated by the authors in VAr planning by SVC based on single objective and multi-objective functions [9-10]. Also, the ability of modal analysis is investigated where this method meets difficulties in placing SVC optimally [9]. This paper investigates the applicability of the Immune algorithm (IA) in the VAr planning problem with STATCOM. Also, other objective

function, known as cost, is added to the objective function used in [10]. The VAr planning problem is formulated as a multi-objective optimization problem for maximizing fuzzy performance indices, which represent minimizing voltage deviation, 2RI losses and the cost of installation resulting in the maximum system VAr margin. To validate the results obtained by the IA, the problem is solved by GA.

2 Immune Algorithm and Genetic Algorithm

A brief explanation of IA and GA is given below:

2.1 Immune Algorithm The immune algorithm (IA) has desirable characteristics as an optimization tool and offer significant advantages over traditional methods. The IA may be used to solve a combinatorial optimization problem. In the IA, antigen represents the problem to be solved. An antibody set is generated where each member represents a candidate solution. Also,

Malihe M. Farsangi, Hossien Nezamabadi-pour Electrical Engineering Department of Shahid Bahonar University, Kerman




29-31 Aug 2007


643

Allocation of Static Var Compensator Using Gravitational Search Algorithm

Abstract: Gravitational optimization (GO) is used to place the Static Var Compensator (SVC) in a large power system based on its primary function, where the optimization is made on two parameters: its location and size. The primary function of a SVC is to improve transmission system voltage, thereby enhancing the maximum power transfer limit. To validate the results, Particle Swarm Optimization (PSO) Algorithm is applied and the performances of GO and PSO are compared. The results show GO quickly finds the optimal solution in finding the location and size of SVC. Keywords: Gravitational optimization, particle swarm optimization, voltage stability, FACTs devices, SVC. 1 Introduction In the last decades, efforts have been made to find the ways to assure the security of the system in terms of voltage stability. It is found that flexible AC transmission system (FACTS) devices are good choices to improve the voltage profile in power systems that operate near their steady-state stability limits and may result in voltage instability. Many studies have been carried out on the use of FACTS devices in voltage and angle stability. Taking advantages of the FACTS devices depends greatly on how these devices are placed in the power system, namely on their location and size. Over the last decades there has been a growing interest in algorithms inspired from the observation of natural phenomena. It has been shown by many researches that these algorithms are good replacement as tools to solve complex computational problems such as optimization of objective functions, training neural networks, tuning fuzzy membership functions, machine learning, system identification, control, etc. Various heuristic approaches have been adopted by researches including genetic algorithm, tabu

search, simulated annealing, ant colony and particle swarm optimization. These algorithms have been proven to be very effective for static and dynamic optimization problems. Study on the use of heuristic approaches to seek the optimal location of FACTS devices in a power system is carried out by the researches around the world [1-10]. In this paper a new optimization algorithm is used known as Gravitational Optimization (GO). The proposed optimization algorithm is based on gravitational law and laws of motion based on following definition by English mathematician Sir Isaac Newton in 1687: every particle in the universe attracts every other particle with a force that is directly proportional to the product of their masses and inversely proportional to the square of the distance between them. GO algorithm was introduced by Rashedi in 2007 [11]. Now in this paper the ability of the proposed algorithm in power system for Var planning by SVC is investigated. To validate the results obtained by GO, PSO is applied and the

Esmat Rashedi , Hossien Nezamabadi-pour, Saeid Saryazdi, Malihe M. Farsangi Electrical Engineering Department of Shahid Bahonar University, Kerman

[email protected], [email protected], [email protected], [email protected]



29-31 Aug 2007


649

Using Genetic Algorithm for Supply Chain Network Optimization Farshad Varasteh

Iran University of Science and Technology [email protected]

Abstract: Supply chain networks(SCN), consisting of manufacturers, distributors, retailers, and consumers, provide the critical infrastructure for the production of goods, their distribution, and their ultimate consumption in today’s globalized economies and societies. The network design problem is one of the most comprehensive strategic decision problems that need to be optimized for long-term efficient operation of whole supply chain. Supply chain network design is to provide an optimal platform for efficient and effective supply chain management. It usually involves multiple and conflicting objectives such as cost, service level, resource utilization, etc. This paper proposes a solution procedure based on genetic algorithms to find the set of Paretooptimal solutions for multi-objective SCN design problem. Finally, the algorithm is examined on an artificial company willing to develop its supply chain network and results are of satisfactory. Keywords: Supply chain Management, Genetic algorithm, Multi-objective optimization, Supply chain network. 1 Introduction Supply chains are characterized by decentralized decision-making associated with the different economic agents but are, in fact, complex network systems. Hence, any formalism that seeks to model supply chains and to provide quantifiable insights and measures must be a system-wide one and network-based. Indeed, such crucial issues as the stability and resiliency of supply chains, as well as their adaptability and responsiveness to events in a global environment of increasing risk and uncertainty can only be rigorously examined from the view of supply chains as network systems. Supply chain networks, consisting of manufacturers, distributors, retailers, and consumers, provide the critical infrastructure for the production of goods, their distribution, and their ultimate consumption in today’s globalized economies

and societies. The reality of supply chain networks today includes not only competition but also cooperation since decisionmakers in the supply chains must interact not only in terms of the product flows but also in terms of pricing in order to satisfy the consumers. At the same time, decision-makers in supply chains are characterized by their individualized objectives, which may include not only profit maximization, but also risk minimization, as well as the incorporation of environmentally conscious objectives, to various degrees. The concept of supply chain networks is as applicable to services as it is to goods. In recent years, the supply chain network (SCN) design problem has been gaining importance due to increasing competitiveness introduced by the market globalization [14]. Firms are obliged to maintain high customer service levels while at the same time they are forced to reduce cost and maintain profit margins. Traditionally, marketing, distribution, planning, manufacturing, and purchasing organizations along the supply chain operated independently. These organizations have their own objectives and these are often conflicting. But, there is a need for a mechanism through which these different functions can be integrated together. Supply chain management (SCM) is a strategy through which such integration can be achieved. The network design problem is one of the most comprehensive strategic decision problems that need to be optimized for long-term efficient operation of whole supply chain. It determines the number, location, capacity and type of plants, warehouses, and distribution centres to be used. SCN design problems cover wide range of formulations ranged from simple single product type to complex multiproduct one, and from linear deterministic models to complex non-linear stochastic ones [4,7,8,12]. In traditional supply chain management, the focus of the integration of SCN is usually on single objective such as minimum cost or maximum profit. However, there are no design tasks that are single objective problems. [6] proposed a multiobjective genetic optimization procedure for the




29-31 Aug 2007

701

Implementing of A New CMOS Adaptive Neuro Fuzzy Logic Controller (FLC) Chip

Abstract: In this paper, we present away of using application of neuro fuzzy inference system (Anfis) architecture to implement a new fuzzy logic controller chip. Anfis which tunes the fuzzy inference system with a backpropagation algorithm based on collection of input-output data makes fuzzy system to learn. This training is given from a standard response of the system and membership functions are suitably modified. For adaptive Anfis based fuzzy controller and its circuit design, we propose new circuits for implementing each controller block, and illustrate the test results and control surface of Anfis controller along with CMOS fuzzy logic controller using Matlab and Hspice software respectively. For implementing controller according to Anfis training, we proposed new and improved integrated circuits which consist of Fuzzifier, Min operator and Multiplier/Divider. The control surfaces of controller are obtained by using Anfis training and simulation results of integrated circuits in less than 0.075mm2 area in 0.35μm CMOS standard technology. Keywords: Anfis, Fuzzy controller chip, CMOS, Neural Network, Backpropagation and Hybrid Algorithm 1 Introduction In the effort to realize intelligent brain-like information processing functions, such as association, perception, and recognition, one very important and challenging approach is to mimic brain functions and structures. In the brain, a neuron receives many electric impulses via a few thousand synapses, and it outputs spike pulses. A typical neuron has three parts: dendrites, a soma, and an axon. Pulse signals called spikes are fed into the dendrites via synapses, the effects of the inputs are gathered up at the soma, and a spike pulse goes to the axon as the output [9]. To analyze and apply neuronal information processing, it is essential to model real neurons. Artificial neural networks started when McCulloch and Pitts in 1943 developed their model of an elementary computing neuron and when Hebb in 1949 introduced his learning rules. A decade latter Rosenblatt introduced the perceptron concept. In

the early sixties Widrow and Holf developed intelligent systems such as ADALINE and MADALINE. The publication of the Mynsky and Paper in 1969 publisehed the book with some discouraging results, that stopped the fascination of artificial neural networks for sometime, and even achievements in the mathematical foundation of the back propagation algorithm by Werbos in 1974 went unnoticed. The current rapid growth of the neural network area started in 1982 with Hopfield recurrent network and Kohonen unsupervised training algorithms. The backpropagation algorithm described by Rumelhard in 1986 caused rapid development of neural networks. [3] Artificial Neural Networks (ANNs) enjoy some distinguished characteristics and are composed of simple elements operating in parallel and including the ability to learn from data, to generalize patterns in data, and to model nonlinear relationships.

Gh. Yosefi Department of

Microelectronic Laboratory of Urmia

University, Urmia 57159, Iran

[email protected]

A. Khoei Departement of Microelectronic

Laboratory of Urmia University, Urmia 57159,

Iran [email protected]

Kh. Hadidi Departement of Microelectronic

Laboratory of Urmia University, Urmia 57159,

Iran [email protected]

S. Aminifar Scientific staff of

Mahabad Islamic Azad University

[email protected]



29-31 Aug 2007


743

A High-Resolution and Low-Power Maximum Circuit for Application in Fuzzy Systems

Taghi Taghizade Abdollah Khoei Khairollah Hadidi

Microelectronic research labratory of urmia university [email protected]

Abstract: A CMOS modular high-resolution and low-power voltage-mode Maximum circuit is presented. The proposed technique also allows straightforward implementation of Minimum circuit. In this structure a latched comparator circuit is used to determine full-level logics to recognize the maximum voltage between two input voltages. This comparator uses a positive feedback mechanism to generate the analogue input signal in to a full- scale digital level. Then with some transmission- gates the maximum voltage is placed at the output of cell. The circuit has been implemented in 0.35µm standard CMOS technology with 2 volts power supply. Simulation results determine a maximum clock frequency of 167MHz for comparator with 1mv Maximum circuit resolution and 100µw power consumption per cell. Keywords: Maximum circuit, Based on Latched comparator, low power, high resolution, fuzzy systems. 1 Introduction Maximum circuits, vitality part of fuzzy systems and neural networks, identify the highest signal intensity between two inputs. They have been widely used in several areas such as data compression, image processing, self organizing networks and vector quantization [1], [2], [3]. Circuit performances can be measured in terms of speed, resolution and power consumption. Many Maximum circuit architectures have been proposed in the literatures. There are two broad methods to implementation of maximum circuits. First method is current mode method. The current mode structures use the current signal as the carrier of information. They are easier to implement since the current signal can be added simply by wiring two signal lines together [4]. Voltage mode is the second method. Its structures have one potential advantage over current mode designs. In current mode structure, in order to sustain information, a current must flow dissipating the energy. In voltage mode structures, the voltage can be maintained on capacitive storage elements practically without dissipating energy, provided the leakage current is neglected. This paper presents a high-resolution and low-power voltage mode Max circuit based on latched comparator, also a Min circuit. The proposed Max circuit uses a

differential CMOS latched comparator to select the maximum voltage. Latched comparators consist of two stages. First stage is a preamplifier with infinite gain and second is a digital latch circuit. Since the amplifiers used in comparators don’t need to be either linear or closed loop, they can incorporate positive feedback to attain virtually infinite gain [5]. Considering the limited gain in the implementation of actual preamplifier design, the actual latched comparators employ an amplifier circuit with infinite gain and a positive feedback latched circuit. In order to aforementioned features of latched comparators we can obtain high resolution. Because by applying positive feedback, circuit gain becomes higher and consequently higher systematic resolution will obtain. Furthermore, this paper presents a low power architecture for Max circuit. 2 Comparator Circuit Description Figure 1 shows the electrical schematic of latched comparator topology. It comprises a differential preamplifier, a voltage controlled flip-flop and a bias generation circuit [6], [7]. When clock is high transistor M10 is switched-on and each outputs of latch circuit has been pulled to different or same



29-31 Aug 2007


749

A High Speed, Low Power Four-Quadrant CMOS Multiplier in Current-Mode to Realize the Simplified Center-of-Gravity Defuzzifier

Abstract: In this paper a new CMOS current-mode four-quadrant analog multiplier based on squarer circuit is proposed which is applicable for realization the Center-of-Gravity defuzzification strategy. The major advantages of this work are low power consumption, high speed and high precision. Current mode realization of the circuits leads to simple configurations. The circuit is designed and simulated using HSPICE simulator by level 49 parameters (BSIM3v3) in 0.35μm standard CMOS technology. The simulation results of defuzzifier demonstrate a linearity error of 1.1%, a THD of 0.97% in 1MHz, a -3dB bandwidth of 41.8MHz and a maximum power consumption of 0.34mW. Keywords: Simplified centroid strategy, CMOS multiplier, Defuzzifier circuit, Fuzzy logic, Squarer circuit. 1 Introduction A fuzzy processor consists of four fundamental units: the so-called fuzzification unit, decision-making logic unit, defuzzification unit and knowledge base. In this paper, we propose an analog current-mode defuzzifier circuit which is based on a squarer circuit. One of the most popular defuzzification methods is the Center-of-Gravity (COG). To realize this method we need two operations: multiplication and division. In the next section we will explain a method in which we will reduce these two operations into one operation, which is multiplication. Then, here we describe multiplication operation or multiplier circuit and review previous works. At present, the power consumption is a key parameter in the designing of high performance mixed-signal fuzzy integrated circuit. The linearity, speed, supply voltage and power dissipation are the main metrics of performance. We try to design specific structures or topologies for the analog multiplier that have high speed, low power dissipation and good linearity for fuzzy application. In multiplier circuit presented in [1], two supply voltages VDD and VSS are required, and also nonlinearity error is considerable. In the other circuit introduced by [3] linearity is good but the power consumption is

high. Some other multipliers [3,9] are not very optimal for low voltage, low-power fuzzy applications. Several techniques of reducing power consumption in CMOS analog multiplier circuits have recently been described. They are the usable floating gate MOS [4], subthreshold mode [5], or class-AB mode [6].They suffer from being highly precise, low power and high speed circuits. This work is a low power, high speed analog multiplier circuit using “dual translinear loops” to realize the COG defuzzifier. In addition, the dual translinear loops allow the design of analog multiplier circuit that exhibit wide bandwidth, high dynamic range and high speed. 2 Circuit Descriptions One of the most popular defuzzification methods is the COG. The general expression of the COG defuzzification can be written as:

∑

∑

=

== n

iyi

n

iyiiy

COG

1

1

μ

μ

(1)

A. Naderi , A.Khoei and Kh. Hadidi Microelectronics Research Laboratory, Urmia University

[email protected] , [email protected] , [email protected]



29-31 Aug 2007


753

A Micropower CMOS Analog Circuit for Gaussian Functions

[email protected] [email protected] [email protected] Abstract: In this paper, a low power CMOS analog circuit that generate the Gaussian function for pattern matching and classification applications is presented. The function is constructed by a novel current mode analog multiplier that is used as a signal squarer and exponential characteristics of MOS transistors in weak inversion. Due to low power consumption, compact structure and wide dynamic range can be easily integrated as a building block of a neural signal processing systems. Keywords: Neural networks, classification and pattern matching algorithms, Gaussian function, neural hardware, analog circuits, translinear loop in weak inversion 1 Introduction Pattern matching and classification are applications where neural algorithms show promising capabilities because neural classifier algorithms can easily handle multidimensional problems [1]. In many neural networks, the algorithm for training is based on probability distributions and pattern matches ranked as probabilities of a match [2]. In many cases these probability density functions can be modeled by normal distributions (or combinations). Although these algorithms primarily implemented in software, but their capabilities to perform many different analog functions such as pattern recognition and image processing make them attractive in hardware implementation. Because of its excellent integration of processing capabilities, the analog approach has been taken in many CMOS neural chips. In this paper a low power analog circuit that produce the Gaussian function for neural or signal processing algorithms is proposed. Other approaches to implement in CMOS technologies the Gaussian function in weak inversion operation [3,4] or as a piece-wise linear

approximation [5] have been reported. The Gaussian function is defined in Equation (1), where x is the input and y the output of the

2

2

2δx

Aey−

= (1)

function and A, σ are adjustable constants which define, respectively, the amplitude and the width of Gaussian function. The function is constructed in three steps. First the input x is squared by means of a novel topology of a current mode multiplier/divider based on translinear loop with MOS transistors operating in weak inversion region and then converted to proportional voltage with a transistor working in linear region, secondly the voltage level shifted to a proper voltage level and finally an exponential obtained with a MOS transistor operating in weak inversion mode completes the transfer function. In Section 2 the novel current mode multiplier/divider circuit presented. In section 3 the Gaussian circuit is reported. Sections 4 and 5 present the mismatch effects and simulation results. Finally the conclusion of this brief is presented.

Azad Mahmoudi Aabdollah Khoei Kheirollah Hadidi Microelectronic Research Centre of Urmia University



29-31 Aug 2007


767

Abstract— In the framework of hybrid position / froce control process, we used a perceptron network with the

extended backpropagation learning algorithm to adjust the parameters of the network. The underlying control system, here a robot, represents a non-linear system with an uncertainty related to it. In the proposed method a perceptron network is used as an approximator for modeling uncertain parts of robot dynamic but we assumed there is known parts through human knowledge and experience. Neural network parameter matrices are updated online with no initial offline training using the error as the objective function. The controller guarantees stability for any arbitrary initial values of neural network parameters and any unknown-but-bounded disturbances. Simulation is dealt with the hybrid control scheme in the Cartesian coordinates of the work space especially from the view point of tracking not only force but also position by citing an example of two degree of freedom robot.

Keywords—Neural Network, Hybrid Position/Force Control, Uncertainty.

I. INTRODUCTION HE major difficulty associated to robot control is dealing with uncertainty in its model. The traditional

representation requires a well-structured and well-defined model.Even if the structure is known, numerical model usually become inefficient as the complexity increases. Moreover,there may be a lot of uncertainties,unpredictable dynamics and other unknown phenomena that can not be mathematically modeled.Therefor, when a system can not be modeled with traditional methods then neural network is a suitable tool that offers an efficient mathematical method in handling many problems like those of stated above.

In the last decades ,some neural network methods to model the dynamic of robot have been suggested.In this filed,Kawato presented in his paper [15] many researchs that are about the use of neural network as a robot controller.

During many tasks, robot makes contact with environment. The problem of controlling robot when

F.Sabahi is with the Electrical Engineering Department, Shahrood

University of Technology(corresponding author to provide e-mail: Farnaz_Sabahi@ yahoo.com).

M.M.Fateh is with the Electrical Engineering Department, Shahrood University of Technology

A.A.Gharehvici is with the Electrical Engineering Department, Shahrood University of Technology

interacting with its environment is called force control. Spong et.al [16] presented an excellent work, which triggered off many researches about robot force control. The most common methods of force control are hybrid position/force control [10], where either a position or a force is controlled along each task space direction, and impedance control [17], that force is controlled indirectly by means of closed-loop position control .

Various applications have been made in the area of robot force control using neural network. Among the pioneering papers are the studies done by Jung et. al [2,11]. They used special properties concerning inertia and friction matrices, and used standard backpropagation algorithm to train the network to achieve zero error. Marques et.al [18] discussed the hybrid impedance control approach with an inverse dynamic controller and a neural network compensator of manipulator. This work was extended by Tian etal [9] .The paper is considered the control of the constrained robotic manipulators and the solution of a reduced model is obtained through a nonlinear transformation and using neural network just for force loop in hybrid control manner. Walter and coworkers [13], developed two neural network algorithm for visuo_motor control of an industrial robot based on visual information provided by two camera ,the robot learns to position its end effector without an external teacher (self organizing algorithm).

Most of methods mentioned above focused on offline training or they have assumed no part of the robot dynamic to be known. Besides that, most of neural

Farnaz Sabahi , M.M.Fateh ,A.A.Gharehvici

Hybrid Robot Controller Based On Neural Network Compensator

T



29-31 Aug 2007


773

A Neuro-Fuzzy Approach for Trajectory Tracking of Two-Link Robot Manipulators

Abstract: This paper presents a neuro-fuzzy scheme for controlling rigid robot manipulators. The proposed control strategy consists of two modules. In first module, RBFN model from the dynamical equations of the plant is acquired to approximate the nonlinear relation between inputs and outputs of the system. In second step, after the neural model obtained, by assigning suitable membership functions, setting heuristic fuzzy rules, and applying gradient descent method for optimization, the fuzzy controller is obtained. Simulations performed on a two-link robot manipulator illustrate the methods and exhibit its performance. The results confirm the accuracy and robustness of controller. Keywords: MIMO systems, Radial basis function network, Fuzzy systems, PID control, Fuzzy control 1 Introduction Robot is one of the most important machines for industrial automation. They can be applied in hazardous environments to substitute manual labors for routine works [1]. To make the robots more effective, their motion trajectory should be manipulated. However, robot manipulators have complex nonlinear dynamical structures and this makes the control action difficult. Also, there are some kinds of uncertainties in nonlinear models of robot manipulators. Some of them are uncertainties in the parameters of the system and some others are not modeled and are due to external disturbances like noise and friction. To encounter these problems, the use of some techniques of soft modeling has great importance. Simulation results obtained from works in [2] and [3], have verified that artificial neural networks are convenient in modeling the nonlinear systems with poorly known dynamics.

On the other hand, fuzzy theory presents outstanding capabilities in the area of controlling nonlinear multi input- multi output (MIMO) systems. In many works like those presented in [4] and [5], fuzzy controllers are used for adaptive control of robot manipulator and the results confirm that fuzzy theory is a reliable method for control action. In this work, we proposed a neuro-fuzzy system that incorporates the human-like reasoning style of fuzzy systems through the use of fuzzy sets and a linguistic model. The main strength of neuro-fuzzy systems is that they are general function approximators with the ability to interpret IF-THEN rules. In other words, we have used the advantages of both neural networks and fuzzy systems in our integrated system. To do this, first of all, we obtain a neural model of the plant using Radial Basis Function Network (RBFN). Then we applied our fuzzy controller to the system and gain satisfactory results. The scheme is evaluated through two experiments. First, we compared the

Matineh Shaker1,*, Caro Lucas1, 2, Amir Homayoun Jafari3 1 Control and Intelligent Processing Center of Excellence, Department of Electrical and Computer

Engineering, University of Tehran, Tehran, Iran 2 Institute for Studies in Theoretical Physics and Mathematics, Tehran, Iran

3 Department of Biomedical Engineering, Amirkabir University of Technology, Tehran, Iran. [email protected]



29-31 Aug 2007


779

Chattering Elimination with Fuzzy Sliding Mode Control in Parallel Robots

M. Dehghani F. Shabaninia Dept. of Elec. Eng. Dept. of Elec. Eng. Shiraz University Shiraz University [email protected] [email protected]

Abstract - Accuracy of tracking and robustness are very important specifications in control of parallel robots. Classical control methods could not satisfy these requirements in parallel robots, simultaneously. Sliding mode control solves problems of accurate tracking, but it is not robust enough because of influence of chattering phenomena. Implementation of fuzzy logic in sliding mode enhances robustness. In this paper, by use of dynamic model of Delta parallel robot and considering uncertainty with dynamic parameters, the fuzzy sliding mode control is applied to this parallel robot. Simulation results and comparison of them with sliding mode control results show the advantages of applying fuzzy logic in control methods.

Keywords: parallel robot, fuzzy logic, sliding mode control, chattering phenomena. 1 Introduction

The idea of design of parallel robots has been regarded since 1947 when D. Stewart designed flight simulator based on his parallel robot [1]. Then other types of parallel robots were designed [2]. In early 80’s Delta parallel robot was presented by Raymond Clavel (figure 1), [3]. The basic idea behind the design of Delta robot is the use of parallelograms. A parallelogram allows an input link to remain at the fixed orientation with respect to the output link [4]. The disadvantage of Delta robots are limited workspace and complex kinematic of them. Because of the appropriate characteristics of Delta parallel robot such as accuracy, high velocity and rigidity, limited workspace can be neglected [3]. These robots are used in quick operations such as picking up and placing light objects (from 10 gr to 1

kg) along trajectories about 200mm long [5], [6], [7] and [8]. Today, some types of Delta robots are constructed which are able to move heavy objects (figure 2). In this paper dynamic based control of Delta robot which involves uncertainty in parameters will be performed using fuzzy sliding mode control.

Figure 1 - The Clavel’s Delta robot



29-31 Aug 2007


785

Fuzzy Meta-Level Control of Snake Robots

Abstract: In this paper, a new fuzzy logic controller (FLC) for navigation of a snake robot is proposed. This FLC is used as high level controller of a novel control architecture. The objective of this control architecture is to guide the snake robot from an initial configuration to a final position. Simple rules in dynamic equations of motion of 2D snake robot moving with serpentine gait are utilized to form a fuzzy inference system. Other parts of the control architecture are a PID as low level controller and a desired orientation generator unit. In order to verify capability of the proposed control architecture to guide snake robot from any initial configuration to desired final position, simulations are carried out using SimMechanic toolbox of MATLAB software. Keywords: snake robot, locomotion, fuzzy logic controller, serpentine gait. 1. Introduction Despite having challenges in the area of control and inefficiency in locomotion due to high friction snake-like robots have attracted the attention of researchers for applications not suitable for wheeled and legged robots. Applications such as ruins of collapsed buildings or narrow passages are good examples where snake robot may be used. Snake-like robots are advantageous over wheeled vehicles for terrainability, traction, universal penetration capabilities, high adaptability and task shapability due to kinematic redundancies. They also offer graceful degradation and increasing reliability when made modular. Other application areas of snake robots are maintenance and condition monitoring of complex technical structures and plants, such as airplane motors, pipelines and nuclear power stations. The two main challenges of snake robots over wheeled mechanisms are difficulty in analyzing and synthesizing snakelike locomotion mechanisms as well as its control. This paper hopes to contribute to these challenges by

applying soft computing methods for the control, particularly fuzzy controllers. Two broad classes of control methods have been used with snake robots. The first class can be described as trajectory-tracking control. It uses predefined gait patterns, usually computed as sine waves that are tracked with a feedback controller [1, 2]. Typically, the control is open-loop: the set points of the joints are calculated and sent to the motor controllers without any form of feedback (the only feedback present in the system is the one used by the PID controller). The other class can be described as online gait generation control. In this case, gaits (motion mode of snake robot) are not predefined in advance, but generated online during locomotion. These approaches can, therefore, better deal with perturbations and irregular terrains. Most of these approaches are model-based, i.e. they rely on a kinematic [3, 4, 5] or dynamic [6, 7] model of the robot’s locomotion in order to design control laws for the gait generation. Another new control method is using central pattern generators (CPGs). In this method locomotion in vertebrates is controlled by CPGs, which are networks of neurons that can produce

S. Hasanzadeh A.-R. Akbarzadeh-T. M.-R. Akbarzadeh-T. Ferdowsi University of Mashhad Ferdowsi University of Mashhad Ferdowsi University of Mashhad [email protected] [email protected] [email protected]



29-31 Aug 2007


793

Gait Planning, Complete Dynamic Modeling and Online Neural Network Control of a Biped Robot

Department of Mechanical Engineering K. N. Toosi Univ. of Technology

S. Ali A. Moosavian S. Hossein Sadati Amir Takhmar Mansoor Alghooneh [email protected] [email protected] [email protected] [email protected]

Abstract: Control of biped robots based on designated smooth and stable trajectories is a challenging problem that is the focus of this paper. A desired trajectory for the lower body will be designed to alleviate the impacts due to contact with the ground. This is obtained by fitting proper polynomials at appropriate break points. Then, the upper body motion is planned based on the Zero Moment Point (ZMP) criterion to provide a stable motion for the biped robot. Next, dynamics equations will be obtained for both single support phase (SSP) and double support phase (DSP). Finally, the online Neural Network Control (NNC) approach is applied for both SSP and DSP. Obtained results show the successful performance of this kind of controller on a biped robot. Keywords: biped robots, stability, gait planning, neural network controller 1 Introduction Control of biped robots requires appropriate gait planning that satisfies stable walking. One of the earliest criteria to investigate the stability of such systems is Zero Moment Point (ZMP) criterion, [1-2]. The ZMP is a point where the horizontal components of the resultant moment of all external forces, including gravity and inertial forces, becomes zero. According to the ZMP criterion if that point is inside the support polygon, the robot will be stable, otherwise the robot will tend to tip over. The support polygon is defined as the foot supporting exterior on the ground. Goswami has introduced the Foot Rotation Indicator (FRI) criterion, [3]. This corresponds to a point where the net ground reaction force would exert to keep the foot stationary. According to this criterion if the FRI point is inside the support polygon, the robot will be stable, otherwise the robot will tend to tip over. The FRI criterion has been introduced only for the SSP. The upper body motion has been used to compensate the stability of biped robots. Vukobratovic has used the prescribed synergy method to obtain the upper body motion, [4].

According to the synergy method, the nonlinear differential equations for the upper body motion are obtained and solved by the iteration method. To obtain the nominal required torques or the required torques for the control of biped robots, it is necessary to obtain theirs dynamic equations. The dynamic equations of biped robots are different in each phase and because of the complexity of equations in DSP, the most of researchers have only investigated these robots in SSP, [5, 6]. To track planned trajectories, various control strategies have been suggested and implemented on the biped robot, [5,6,7,8,10]. Among different controllers, the Sliding Mode Control (SMC) is a suitable control approach that ensures good tracking despite parameter uncertainties, [5, 8, 10]. The two CTM and SMC have been applied for the single support phase (SSP) of a 5 DOF biped robot without active feet, where SMC results in a better performance compared to CTM, [5]. However, SMC experiences chattering problem that is due to switching process and may even cause instability, so some researcher has tried to eliminate chattering problem in the control of a biped robot,



29-31 Aug 2007


805

A Bio-inspired Genetic Algorithm Applied to a Constrained Optimization Problem in Power Systems

Abstract: In this paper, an improved genetic algorithm is proposed to solve the economic dispatch (ED) problem for co-generation systems. The proposed algorithm is a novel bio-inspired Genetic Algorithm. This algorithm seems to be efficient in finding global optimum in the economic dispatch problem. Furthermore, it provides a suitable framework for future extension to other optimization algorithms.

Keywords: Genetic Algorithm, Economic Dispatch.

1 Introduction

Economic dispatch (ED) is used to determine the optimal schedule of on-line generating outputs so as to meet the load demand at the minimum operating cost. Recently, co-generation units have played an increasingly important role in the utility industry. Co-generation units can provide not only electrical power but also heat to the customers. For most cogeneration units, the heat production capacities depend on the power generation and vice versa. Some complications arise in Combined Heat and Power (CHP) systems because the dispatch has to find the set points of power and heat production with the minimum fuel cost such that both demands were matched, indeed, the CHP units should operate in a bounded power vs. heat plane [1–9]. Basically, the dispatch problem can be formulated as an optimization problem with a quadratic objective function and linear constraints. Such problems can be solved with a general-purpose package that is designed to solve quadratic programming problems, but the computational effort increases at least quadratically with the increasing number of units. The literature reports basically the traditional method to solve the ED problem adapted for CHP plants based on Lagrangian relaxation [1], [2]. However,

each author adds some new feature to arrive to the optimal solution. For example [1] solves the CHP economic dispatch problem based on the separability of the objective function of the problem. The separability, defined by the authors, is the fact that the objective function is the sum of the cost functions of separate units, and most of the constraints are linked to one specific unit. In this method, a two-level strategy was adopted. The lower level solves the economic dispatch problems of the individual units for given power and heat lambdas, and the upper level updates the lambda’s by sensitivity coefficients. The procedure is repeated until the heat and power demands are met. Ref. [2] does a physical interpretation of the feasibility region for the CHP units, and then solves the problem in two layers, one for heat and the other for power. Ref. [3] uses the same method as [2] but adds a steam turbine working at full capacity. A new algorithm for combined heat and power economic dispatch (CHPED) problem was proposed in [4]. In this algorithm the problem was decomposed into heat and power dispatch sub-problems. The two sub-problems were connected by the heat-power feasible region constraints of co-generation units. The analysis and interpretation of the connection have led to the development of the two-layer algorithm in which the outer layer used the Lagrangian relaxation technique to solve the power dispatch, and the inner layer used

H. R. Abdolmohammadi

[email protected]

S. Jafari

[email protected]

M. R. Rajati [email protected]

M. E. Nazari

[email protected]



29-31 Aug 2007


29-31 Aug 2007


813

Reactive power planning in Distribution Systems using A Reinforcement learning method

Mehdi Ahrari Nouri ,Alireza Seifi

[email protected] , [email protected]

Ms Student Assistance Professor Department of Electric Engineering Department of Electric Engineering

Shiraz University Shiraz University Shiraz (Iran) Shiraz (Iran)

Abstract: This work presents a new algorithm RL approach for capacitor allocation in distribution feeders. The problem formulation considers two distinct objectives related to total cost of power loss and total cost of capacitors including the purchase and installation costs. The formulation is a multi-objective and non-differentiable optimization problem. The proposed method of this article uses RL for sizing and sitting of capacitors in radial distribution feeders. The proposed method has been implemented in a software package and its effectiveness has been verified through a 9-bus radial distribution feeder along with a 34-bus radial distribution feeder for the sake of conclusions supports. A comparison has been done among the proposed method of this paper and similar methods in other research works that shows the effectiveness of the proposed method of this paper for solving optimum capacitor planning problem. Keywords:Reactive Power Planning, Reinforcement Learning, Radial Distribution Feeder 1 Introduction Capacitors are widely installed in distribution systems for reactive power compensation to achieve power and energy loss reduction, voltage regulation, system capacity release, power flow control, improving system stability and power factor correction. Capacitor planning must determine the optimal site and size of capacitors to be installed on the buses of a radial distribution system. Many approaches have been proposed to solve the capacitor planning problem. For instance, [1] formulated the problem as a mixed integer programming problem that incorporated power flows and voltage constraints. The problem was decomposed into a master problem and a slave problem to determine the sitting of the capacitors, and the types as well as size of the capacitors placed on the system. Refs [2,3] proposed heuristic

approaches to identify the sensitive nodes by the levels of effect on the system losses. Ref. [4] adopted an equivalent circuit of a lateral branch to simplify the distribution loss analysis, which obtained the capacitor operational strategies according to the reactive load duration curve and sensitivity index. Moreover, optimal capacitor planning based on the fuzzy algorithm was implemented to present the imprecise nature of its parameters or solutions in practical distribution systems [5-7]. Several investigations have recently applied AI techniques to resolve the optimal capacitor planning problem due to the growing popularity of AI. Refs. [8, 9] presented a solution methodology based on a simulated annealing (SA) technique. Ref. [10] applied the tabu search technique to determine the optimal capacitor planning in Chiang et al's [8] distribution system, and compared the results of the TS with the SA. In Refs.[11-12], genetic algorithms (GA) were



29-31 Aug 2007


835

Fuzzy Accuracy-based Classifier Systems for EEG Classification of Schizophrenic Patients

M. Sabeti*, M. H. Sadreddini*, G. W. Price+

*Department of Computer Science and Engineering, School of Engineering, Shiraz University, Shiraz, Iran

+ School of Psychiatry and Clinical Neuroscience, University of Western Australia, Perth, Australia

[email protected]

Abstract: In this paper, EEG signals of twenty schizophrenic patients and twenty age-matched healthy subjects are analyzed with objective of classification two groups. In this case, Fuzzy Accuracy-based Classifier System (F-XCS) is used to automatically generate fuzzy if-then rules for discrimination healthy and schizophrenic subjects. Several features including AR model coefficients, band power and fractal dimension are extracted from EEG signals. First, the F-XCS is applied where a randomly generated initial population of fuzzy if-then rules is evolved by typical genetic operations such as selection, crossover and mutation. Second, a heuristic procedure for improving the performance of F-XCS is applied and result of adding this heuristic procedure is analyzed. The motivation behind this approach is that F-XCS will be capable of generating compact, high performance rule sets which are general and accurate. Keywords: EEG, Schizophrenic, Fuzzy, Classification. 1 Introduction Schizophrenia is a mental disorder from which 1% of the whole population suffer. According to the diagnostic criteria of the American Psychiatry Association [1], patients show some characteristic symptoms including delusions, hallucinations or disorganized speech. Recently, much attention has been paid to analysis of EEG signals of schizophrenic patients. In some research [2, 3], nonlinear methods have been applied to EEG signals of the two groups of schizophrenic patients and control participants. The results showed differences in dynamic process between the two mentioned groups. Hornero et al. [4] asked the participants to press space bar key randomly to generate time series. The results obtained showed that the time series generated by schizophrenic patients had a lower complexity than the control group. In an interesting test, for random number generation [5], participants were asked to choose a number from one to ten several times. Numbers

had to lack a generative rule that is to be as random as possible. They found that schizophrenic patients were more inclined to be repetitive. Pressman et al. [6] showed lack of synchronization alternation ability in the schizophrenic patients during working memory task. They indicated a difference in brain activity, especially in frontal and temporal channels. Paulus et al. [7] carried out a simple choice task consisting of predicting 500 random right or left appearances of a stimulus in order to obtain binary response in patients with schizophrenia and control group. After applying mutual and cross-mutual information, they showed that the response sequences generated by patients exhibited a higher degree of interdependency than those in control group. 2 Data Acquisition Twenty patients with schizophrenia and twenty age-matched control participants participated in this study. They were recruited from the Center for Clinical Research in Neuropsychiatry, Perth,



29-31 Aug 2007


865

Reflecting on the Fuzzy process of Self-organized Learning

Hamid Sepehr (PhD) Department of Education and Psychology, Yazd University

[email protected]

Abstract : This paper presents the findings of two action research projects involving learning and self-organization by two distinct groups of learners. They include English-speaking primary school children and Farsi-speaking university students. Focusing on recordings of process information it discusses the generally fuzzy nature of the self-organized learning. The findings seem to support a multi-valence - as opposed to the traditional bi-valence approach to the study of learning. The analysis of the process information also depicts a non-linear – as opposed to linear - character for the way learning and self-organization develops. The study of the process of learning also shows a simple causal model to be ineffective in evaluating the influence of different factors in development of learning and stresses the need for alternative and more ‘fuzzy’ approaches such as ‘coherence’ or ‘synchronicity’ to confront the challenges in this field. Fuzzy Cognitive Maps may also be useful in mapping the complex relationship between different modalities of learning. Introduction Learning is placed at the heart of any design for improvement and change. It is at times described as the central theme in psychology (Schultz & Schultz 1987). In the past few decades, educational research and theory has shifted its focus from ‘teaching’ to ‘learning’. Learning may also be the most researched topic within the field of ‘fuzzy logic’ application (e.g. Kosko 1994, p 205). Much of the ‘fuzzy logic’ literature on learning is in the domain of artificial intelligence and machine learning (eg Russo & Jain 2000). However, applications within humanities, psychology and education are not rare.

Traditional models of learning have generally followed a linear and single-mode path focusing on isolated and disperse aspects of

learning (Driscoll 1994). Mechanistic models have reduced the role of awareness and have stressed conditioning. Less attention has been paid to Human Learning as a developmental and multi-modal process. Although the developmental models have attempted to describe the mechanisms of development in given domains (e.g. cognitive, emotional, social, etc.) they have not gone far enough in studying the interrelationship between such domains (op cit & Ho 2001). The cognitive

models have not sufficiently attended to mapping the actual processes people choose to engage in while learning (Marton & Saljo 1976, 1997, Entwistle 2002). Self-management, self-directedness, self-regulation and self-organization are among the concepts most widely used (eg Ginnis 1992, Westwood 1990). Such approaches have strengthened a ‘systems’ view of man as active and ever-searching learner.

Self-Organization as a dynamic control process has been proposed and studied in many domains (Schultz & Schultz 1987, Lovelock 1978, Camzine et al 2003). An approach to ‘learning’ as a process of ‘self-organization’ has been proposed by Thomas and Harri-Augstein (1985). With roots in psychological as well as cybernetic theories, their theory suggests that all effective learning is achieved when a person is consciously engaged in a process of generating useful feedback to himself/herself. They see the process as personal, ‘conversational’ and reflective (Harri-Augstein & Thomas 1991). Self-organized learning (as opposed to ‘other-organised learning’) as a process of human and organizational development has been used widely to help overcome difficulties and to raise effectiveness in diverse areas of learning in life



29-31 Aug 2007


877

A New Method for Automatic Border Detection in IVUS Images and 3D Visualization of the Segmented Frames

Abstract: In this paper, an effective method for automated extraction of the lumen and media–adventitia borders in intravascular ultrasound (IVUS) images is presented. The method is based on non-parametric deformable models. The calcified deposits within an IVUS image appear as bright regions between the two extracted borders and obstruct the penetration of ultrasound, a phenomenon known as “acoustic shadowing”. We have visualized the segmented frames and highlighted the calcified regions in the 3D representation of IVUS images. The proposed method is evaluated using 70 IVUS frames from 7 different patients. Statistical analyses of the results demonstrate a high accuracy rate of the automatically extracted boundaries compared to those manually identified by expert. Keywords: Deformable models, IVUS, Border detection, 3D Visualization. 1 Introduction Intravascular Ultrasound (IVUS) is a catheter-based medical imaging technique. Using a specially designed ultrasound catheter it provides real-time tomographic images of the arterial wall that shows the morphology and histological properties of the cross-section of the vessel. IVUS not only provides a quantitative assessment of the vessels' wall but also introduces information about the nature of atherosclerotic lesions as well as the plaque shape and size [1], [2]. The first step for plaque characterization in IVUS images is segmentation. Nevertheless, it is a difficult, subjective and time-consuming procedure to manually perform segmentation. Therefore, there is an increasing interest in developing automatic tissue segmentation algorithms for IVUS images [3]. Several algorithms for lumen and media-Adventitia contours detection have been reported in the past decade. Various edge detection and contour identification techniques together with

different border optimization algorithms such as dynamic programming, graph searching, simulated annealing, solution of partial differential equations, and genetic algorithms have been applied to the IVUS images in these articles [4], [5]. Recent approaches are mostly based on the active contours together with minimizing an energy or cost function which guides a snake towards the vessel borders. The active contours used in the previous approaches are mostly based on a kind of parametric deformable model. However, parametric deformable models have two main limitations. First, in situations where the initial model and desired object boundary differ greatly in size and shape, the model must be re-parameterized dynamically to faithfully recover the object boundary. The second limitation is that it has difficulty dealing with topological adaptation such as splitting or merging model parts, a useful property for recovering either multiple objects or objects with unknown topology [6]. In this work, we have focused on the development and validation of an automated method based on

Z.Najafi1, A.Taki1, 2, S.K.Setarehdan1, R.Zoroofi1, N.Navab2

1 Faculty of Electrical and Computer Engineering, University of Tehran, Tehran, Iran

2 Computer Aided Medical Procedures (CAMP) - TU Munich, Germany

[email protected], [email protected], [email protected], [email protected], navab@ cs.tum.edu



29-31 Aug 2007


891

Breast Cancer Detection from FNA Using SVM and RBF Classifier

Abstract: In this paper, we consider the benefits of applying support vector machines (SVMs) and radial basis function (RBF) for breast cancer detection. The Wisconsin diagnosis breast cancer (WDBC) dataset is used in the classification experiments; the dataset was generated from fine needle aspiration (FNA) samples through image processing. The 1-norm C-SVM (L1-SVM) and 2-norm C-SVM (L2-SVM) are applied, for which the grid search based on gradient descent based on validation error estimate (GDVEE) are developed to improve the detection accuracy. Experimental results demonstrate that SVM classifiers with the proposed automatic parameter tuning systems and the RBF classifier can be used as one of most efficient tools for breast cancer detection, with the detection accuracy up to 98%. Keywords: Breast cancer detection, Parameter tuning, Radial basis function networks, Support vector machines. 1 Introduction Worldwide, breast cancer is the most common form of cancer and the second most common cause of cancer deaths in females, which affects approximately 10% of all women at some stage of their life in the western world. Breast cancer may be detected via a cautious study of clinical history, physical examination and imaging with either mammography or ultrasound. However, definitive diagnosis of a breast mass can only be established through fine-needle aspiration (FNA) biopsy, core needle biopsy or excisional biopsy. Among these methods, FNA is the easiest and fastest method of obtaining a breast biopsy, and is effective for women who have fluid-filled cysts. FNA uses a needle smaller than those used for blood tests to remove fluid, cells, and small fragments of tissue for examination under a microscope. Research works on the Wisconsin diagnosis breast cancer (WDBC) data grew out of the desire of Dr. Wolberg to diagnose breast masses accurately based solely on FNA. Previously, researchers from

the University of Wisconsin, Madison, applied image processing techniques to derive the WDBC dataset directly from digital scans of FNA slides, and then employed machine learning techniques to differentiate benign from malignant samples, which could be the earliest study of machine learning application to breast cancer detection. Later, several works on computational intelligence were developed in the area of breast cancer, including the multilayer perceptron [1], radial basis function (RBF) networks [2], fuzzy classifiers [3,6], clustering algorithms [4], evolutionary computation [5], principal component analysis [6], and different kernel-based methods [7]. Support vector machines (SVMs) are highly successful in solving various nonlinear and non-separable problems in machine learning, In addition to the original C-SVM learning method proposed by Cortes and Vapnik [8] in 1995. In order to use SVM, one needs to decide the value of the regularization parameter (C for C-SVM) and the kernel function before training the SVM classifier. Thus, choosing a suitable kernel function is imperative to the success of the learning process,

Majid Iranpour , Sanaz Almassi , Morteza Analoui Computer Department , Iran University science & Technology

[email protected] , [email protected] , [email protected]



29-31 Aug 2007


911

Fuzzy Learning Automata: A Novel Approach For Multimodal Function Optimization

Abstract: The concept of fuzzy learning automata (LA) has been introduced to construct a novel algorithm for optimizing the multimodal complex functions. In this approach a fuzzy controller is designed to change the internal LA parameters adaptively while the search process is executing by LA. The proposed algorithm has been tested on different kinds of benchmark functions. The experimental results show more powerfulness and effectiveness of the proposed algorithm in comparison to other function optimization algorithms based on the LA. The proposed algorithm can be considered as an effective search and optimization algorithm and may be utilized for wide range of engineering tasks like data mining, pattern recognition, image processing, adaptive control, power systems, and other optimization problems. Keywords: Fuzzy controller, learning automata, function optimization, reinforcement algorithm. 1 Introduction Function optimization is an important task which deals with finding the minimum (or maximum) value of a function in the search space. Many engineering tasks, such as pattern recognition, data clustering, image processing, power systems, and design of integrated circuits, can be consider as optimization ( or multiobjective optimization) problems. Different kinds of gradient, heuristic, evolutionary and swarm intelligence based algorithms have been reported in the literature. Learning Automata (LA) is another approach which has been utilized for function optimization. Learning automata (LA) is referred to an automaton acting in an unknown random environment which improves its performance to obtain an optimal action. An action is applied to a random environment and the random environment evaluates the applied action and gives fitness to the selected action of automata. The response of the environment is used by automata to select its next action. This procedure is continued to reach the optimal action. LA has been used in several tasks of engineering problems (for example graph partitioning [1] adaptive

control [2], signal processing [3], power systems [4], and pattern recognition [5]). Over the years many researches on the LA based function optimization techniques were reported. A stochastic automata model was adopted by Shapiro and Nerendra [6] to find an optimal solution for multimodal performance criteria. Thathachar and Sastry [7] proposed Pursuit algorithm to improve the convergence rate of LA based function optimization. Also an automata model was proposed by Oommen and Lanctôt [8], using discritized Pursuit algorithm. Obaidat et al [9] developed an algorithm for fast convergence of learning automata. Beigy and Meybodi [10] proposed a continuous action-set automaton for function optimization. They studied the convergence properties of their algorithm theoretically and experimentally. Also Zeng and Lui [11] presented a method for optimizing continuous functions using LA. Their method enhances local search in interesting regions or intervals and reduces the whole searching space by removing useless regions. All aforesaid algorithms have some internal parameters with very important influence on the search process of the method. Obviously an intelligent schedule for controlling these

Seyed-Hamid Zahiri

Department of Electrical Engineering, Faculty of Engineering, Birjand University, Birjand, Iran

[email protected]



29-31 Aug 2007


937

Gait Recognition Based on Human Leg Gesture Classification

Jaber Roohi, Hadi Sadoghi Yazdi

Engineering Department, Tarbiat Moallem University of Sabzevar, Sabzevar, Iran E-mail: [email protected]

Abstract: This paper presents a human gait recognition system based on a leg gesture separation. Main innovation in this paper includes gait recognition using leg gesture classification which gives a high precision recognition system. Five state of leg in human gait are extracted after background estimation and human detection in the scene. Leg gestures are classified over directional chain code of bottom part of silhouette contour. A spatio-temporal data base namely Energy Halation Image (EHI) is constructed over bottom part of human silhouette from train film sequence for five leg gestures separately. Eigen space of energy halation is applied to multilayer perceptron neural network. Five neural network system recognize people but with medium recognition rate. A neuro-fuzzy fusion technique is used for obtaining high recognition rate. Experimental results is performed over a suitable data base include 20 samples for eight person which each sample have 100 frames approximately. 99% recognition rate of the proposed system is obtained over 10 samples test patterns. Keywords: Human leg gesture separation; Gait recognition; Background estimation; Spatio-temporal data base; Neural network classifier; Neuro-fuzzy based classifier fusion.

1. Introduction UMAN GAIT is an important subject in various researches. Some of them attend to gait as a biometric feature in human

identification problem [1]. Human gait recognition has attracted growing attention in video-based applications [2, 3]. Recent research has shown that individuals have distinctive and special ways of walking and that human gait recognition has many advantages as human gait is a biometric feature that may be captured from a great distance and gait has the advantage of being unobtrusive. Various applications exist for gait analysis as designing of suitable recessed tactile surface [4].

Tactile ground surface indicators installed on sidewalks help visually impaired people walk safely. The visually impaired distinguish the indicators by stepping into its convexities and following them. However, these indicators sometimes cause the nonvisually impaired to stumble. In [4] have been studied effects of these indicators by comparing the kinematics and kinetic variables of walking on paths with and without indicators.

Another interest for gait identification is that of reflect gait degeneration due to ageing that might have closer linkage to the causes of falls. This would help to undertake appropriate measures to prevent falls. Like in many other developed countries, falls in older population

has been identified as a major health issue in Australia [5]. In [6] automatic recognition of young-old gait types from their respective gait-patterns has been studied using support vector machine. Ageing influences gait patterns causing constant threats to control of locomotors balance.

Biomechanical analysis of gait has been successfully applied in human clinical gait analysis [7]. With regards to gait recognition, a major early result from Psychology is by Johansson [8], who used point light displays to demonstrate the ability of humans to rapidly distinguish human locomotion from other motion patterns. Cutting and Kozlowski [9] showed that this ability also extends to recognition of friends.

Identification of people by analysis of gait patterns extracted from video has recently become a popular research problem. However, the conditions under which the problem is “solvable” are not understood or characterized as are mentioned in [3]. The biggest limitation in human motion analysis is the underlying difficulty of tracking the human body for subsequent interpretation [10, and 11].

So, we propose new approach without body parts tracking which fall into motion-based category. Main innovation of the proposed method includes gait recognition based of leg gesture classification. Leg gesture studies have various applications. In this among, some interest work indicates importance of leg gesture

H




949

Road Detection from High Resolution Satellite Imagery Using Texture Parameters in Neural Network

M. Mokhtarzade

PhD Student, K.N Toosi University of Technology, Geodesy and Geomatics Faculty ([email protected])

H. Ebadi Assistant Professor, K.N Toosi University of Technology, Geodesy and Geomatics Faculty

([email protected]) M.J.Valadan Zoej

Associate Professor, K.N Toosi University of Technology, Geodesy and Geomatics Faculty ([email protected])

Abstract: In this paper, neural networks are applied on high resolution IKONOS images for road detection. It was tried to optimize neural network's functionality using a variety of texture parameters with different window sizes and gray level numbers. Both the source image and pre-classified image were used for texture parameter extraction. The obtained results were compared in terms of road and background detection accuracy. It was concluded that using texture parameters from the source image could improve road detection ability of the neural networks, while using the results of texture analysis of the pre-classified image develops the background detection accuracy. Keywords: Road detection, texture parameters, co-occurrence matrix, neural networks, back propagation. 1 Introduction High resolution commercial satellite lunches have made available imagery at resolutions close to that of aerial photographs, which can then be used in wide variety of applications such as preparing and updating maps. Extraction of the road networks was mostly carried out manually by the operators so far. However, considerable skill was necessary for such operations, efficiency was never very high, and this method is costly and time consuming. Road detection can be considered as the first step in road extraction process and is defined as the process of assigning a value to each pixel that can be used as a criterion to extinguish road and non-road pixels. Vigorous methods have been proposed for automatic and semi-automatic extraction of road networks from satellite images. Recently, these methods are more focused on high resolution satellite images due to their outstanding characteristics in mapping from space.

A comprehensive review on the proposed methods for road extraction could be found in [1] where these methods are categorized from different aspects and a broad reference list is presented. The idea of geometrical and topological analysis of high resolution binary images for automatic vectorization of segmented road networks was presented in [2]. In [3] a new fuzzy segmentation method is proposed for road detection in high resolution satellite images that needed only a few number of road samples. Recently, the idea of using contextual information for improving segmentation process of road regions have been tested by many researchers. As a good example of exploiting texture information in road extraction, the research presented in [4] could be mentioned. Also, in [5], the effectiveness of angular texture signature was evaluated to discriminate between parking lots and roads using high resolution satellite images. In the present research, road detection is performed on high-resolution pan-sharpened RGB Ikonos satellite images, using texture parameters in artificial neural network algorithms. At first, road detection has been performed using only spectral information. Then




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