comparison of various techniques for software effort ... · comparison of various techniques for...

International Journal On Advanced Computer Theory And Engineering (IJACTE)

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ISSN (Print): 2319-2526, Volume -4, Issue -4, 2015

1

Comparison of various Techniques for Software Effort Estimation

1RshmaChawla,

2Deepak Ahlawat

1,2 MMICTBM, MMU Mullana

Email: [email protected],

[email protected]

Abstract: The most significant activity in software project

management is Software development effort prediction.

Software development effort estimation is the process of

predicting the most realistic use of effort required for

developing software based on some parameters. Software

effort estimation at early stages of project development

holds great significance for the industry to meet the

competitive demands of today’s market. In this paper,

software development effort estimation using Fuzzy

Triangular Membership Function, GBell Membership

Function, Gauss2 Membership Function and Trapezoidal

Membership Function is implemented using Mamdani

Type Fuzzy inference system of Fuzzy Logic Toolbox

Software of Matlab 7.5 and the results of these

membership functions are compared with each other and

with COCOMO model. It is found that the Fuzzy Logic

Model using Trapezoidal Membership Functionprovided

best results. However, if transition between the phases is

smoothly desirable, then Gauss2 Membership Function

gives better result then GBell Membership Function. The

criterion chosen for comparing the results is Mean

Magnitude of Relative Error (MMRE).

Keywords:Software Effort Estimation, Fuzzy Logic,

COCOMO Model, Membership Functions, NASA63

dataset.

I. INTRODUCTION

Software development is the computer programming,

documenting, testing, and bug fixing involved in

creating and maintaining applications and frameworks

involved in a software release life cycle and resulting in

a software product.

1.1. Software Development EffortEstimation

Software effort estimation is the prediction of the likely

amount of cost, time, and staffing levels required to

build a software system at an early stage during a

project. It is difficult to obtain the effort estimate during

the preliminary stages, because of the limited resources

available at that time [7].

1.2. Need for Effort Estimation

1. It would facilitate increased control of time and

overall cost benefit in software development life cycle.

2. Software development effort estimates are the

basis for project bidding and planning.

3. Software effort estimation has even been

identified as one of the three most demanding challenges

in software application areas. During the development

process, the cost and time estimates are useful for the

initial rough validation and monitoring of the project’s

completion process. And in addition, these estimates

may be useful for project productivity assessment

phases.

1.3. Size Estimation

The estimation of size is very critical and difficult area

of project planning. It has been recognized a crucial step

from the very beginning. Metric used for size estimation

is the Source Lines of Code.A line of code is any line of

program text that is not a comment or a blank line,

regardless of the number of statements or fragment of

statements on the line. This specially includes all lines

containing program header, declarations, and executable

and non-executable statements.Unit of measurement is

KLOC (Kilo lines of code).

There are several cost, schedule, and effort estimation

models which use LOC as an input parameter, including

the widely-used Constructive Cost Model (COCOMO)

invented by Barry Boehm [7].

1.4. COCOMO Model

The Constructive Cost Model (COCOMO) is an

algorithmic software cost estimation model

developed by Barry W. Boehm.

COCOMO was first published in Boehm’s 1981

book Software Engineering Economics as a

model for estimating effort, cost, and schedule

for software projects. COCOMO is a model that

allows one to estimate the cost, effort, and

schedule when planning a new software

development activity.

This model estimates the total effort in terms of

“person – months” of the technical project staff.

COCOMO is a hierarchy of software cost

estimation models, which include basic,

intermediate and detailed sub models.

Boehm proposed 3 modes of projects:


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1. Organic mode – simple projects that engage small

teams working in known and stable environments.

2. Semi-detached mode– projects that engage teams with

a mixture of experience. It is in between organic and

embedded modes.

3. Embedded mode– complex projects that are

developed under tight constraints with changing

requirements.

1.4.1. Intermediate COCOMO Model

The basic model initially developed by Barry Boehm

allowed for a quick and rough estimate, but it resulted in

a lack of accuracy. So Boehm introduced (reduced large

number of candidate factors down to relatively

manageable number of factors which can be used for

practical software cost estimation) resulting set of 15

factors (predictors), or cost driver attributes. This model

is referred as Intermediate COCOMO Model or

COCOMO II.

The cost drivers are grouped into following four

categories [7, 23]

1. Product attributes

(a) Required software reliability (RELY)

(b) Database size (DATA)

(c) Product complexity (CPLX)

2. Computer attributes

(a) Execution time constraints (TIME)

(b) Main storage constraints ( STOR)

(c) Virtual Machine volatility (VIRT)

(d) Computer Turnaround time (TURN)

3. Personal Attributes

(a) Analyst capability (ACAP)

(b) Application experience (AEXP)

(c) Programmer capability (PCAP)

(d) Virtual machine experience (VEXP)

(e) Programming language experience (LEXP)

4. Project attributes

(a) Modern programming practices (MODP)

(b) Use of software tools (TOOL)

(c) Required development schedule (SCED)

Each of these cost driver attributes determines a

multiplying factor which estimates the effect of the

attribute on software development effort. These

multipliers are applied to nominal COCOMO

development effort estimate to obtain a refined estimate

of software development effort [23].

Table 1.1: Intermediate COCOMO nominal effort

estimating equations

Development Mode Nominal Effort Equation, Ei

Organic

Semi-Detached

Embedded

(MM)NOM = 3.2(KDSI)1.05

(MM)NOM = 3.0(KDSI)1.12

(MM)NOM = 2.8(KDSI)1.20

Table 1.2:Effort multipliers for different cost drivers

S. No Cost Driver Symbol Very Low Low Nominal High Very High Extra High

1 RELY 0.75 0.88 1.00 1.15 1.40 -

2 DATA - 0.94 1.00 1.08 1.16 -

3 CPLX 0.70 0.85 1.00 1.15 1.30 1.65

4 TIME - - 1.00 1.11 1.30 1.66

5 STOR - - 1.00 1.06 1.21 1.56

6 VIRT - 0.87 1.00 1.15 1.30 -

7 TURN - 0.87 1.00 1.07 1.15 -

8 ACAP - 0.87 1.00 1.07 1.15 -

9 AEXP 1.29 1.13 1.00 0.91 0.82 -

10 PCAP 1.42 1.17 1.00 0.86 0.70 -

11 VEXP 1.21 1.10 1.00 0.90 - -

12 LEXP 1.14 1.07 1.00 0.95 - -

13 MODP 1.24 1.10 1.00 0.91 0.82 -

14 TOOL 1.24 1.10 1.00 0.91 0.83 -

15 SCED 1.23 1.08 1.00 1.04 1.10 -

The multiplying factors for all 15 cost drivers are

multiplied to get the effort adjustment factor (EAF). The

final effort estimate, E, is obtained by multiplying the

initial estimate by the EAF.

That is,

Development Effort = EAF * Ei ....(1)

1.5. Fuzzy Logic Approach

Since fuzzy logic foundation by LotfiZadeh in 1965, it

has been the subject of important investigations [15, 16].

It is a mathematical tool for dealing with uncertainty and

also it provides a technique to deal with imprecision and

information granularity. The fuzzy logic model uses the

fuzzy logic concepts introduced by LotfiZadeh. Fuzzy

reasoning consists of three main components:


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fuzzification process, inference from fuzzy rules and

defuzzification process. Fuzzification process is where

the objective term is transformed into a fuzzy concept.

The membership functions are applied to the actual

values of variables to determine the confidence factor or

membership function (MF). Fuzzification allows the

input and output to be expressed in linguistic terms.

Inferencing involves defuzzification of the conditions of

the rules and propagation of the confidence factors of

the conditions to the conclusion of the rules. A number

of rules will be fired and the inference engine assigned

the particular outcome with the maximum membership

value from all the fired rules.

1.6. Parameters Analysis

The main parameter for the evaluation of cost estimation

models is the Magnitude of Relative Error (MRE) which

is defined as follows

Magnitude Relative Error (RE) = ˆE E

E

Where E = Estimated Effort, E =Actual Effort.

The MRE value is calculated for each observation i

whose effort is predicted. The aggregation of MRE over

multiple observations (N) can be achieved through the

Mean MRE (MMRE) as follows:

………………… (2)

Lower value of MMRE is better [24].

II. FUZZY IDENTIFICATION

A fuzzy model [6] is used when the systems are

notsuitable for analysis by conventional approach or

when theavailable data is uncertain, inaccurate or vague

[15, 17]. The pointof Fuzzy logic is to map an input

space to an output spaceusing a list of if-then statements

called rules. All rules areevaluated in parallel, and the

order of the rules is unimportant.For writing the rules,

the inputs and outputs of the system areto be identified.

To obtain a fuzzy model from the dataavailable, the

steps to be followed are:

1. Select a Mamdani type Fuzzy Inference system.

2. Define the input variables mode, size and output

variableeffort.

3. Set the type of the membership functions (TMF

orGBellMF orGauss2 or Trapezoidal).

4. Write the appropriate fuzzy rules in Rule editor.

5. Select the Rule viewer and calculate the estimated

fuzzy effort.

The framework is shown in “Fig. 2.1”.

Figure 2.1: Fuzzy Framework for Effort Estimation

MODE

Estimated

SIZE Effort

Fuzzy Rules

In FIS, first gives the range of MODE of the project for

particular Membership Function then gives the range for

the SIZE. The range of Development Effort is the Actual

Effort given in the NASA63 dataset.

2.1. Fuzzy Rules

Our rules [24] are based on the fuzzy sets of MODE,

SIZE and EFFORT appears in the following form:

If MODE is Organic and SIZE is S1 then EFFORT is

EF1

If MODE is Semidetached and SIZE is S1 then

EFFORT is EF2

If MODE is Embedded and SIZE is S1 then EFFORT is

EF3


EF4

If MODE is Semidetached and SIZE is S2 then

EFFORT is EF5


EF5


EF3


EF4


EF6


EF4

---------------------------------------------------

This is represented in MATLAB as shown in figure

below:

Figure 2.2: Fuzzy Rules

FIS


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2.2.Membership Functions

A membership function (MF) is a curve that defines how

each point in the input space is mapped to a membership

value (or degree of membership) between 0 and 1. The

input space is sometimes referred to as the universe of

discourse, a fancy name for a simple concept.One of the

most commonly used examples of a fuzzy set is the set

of tall people. In this case the universe of discourse is all

potential heights, say from 3 feet to 9 feet, and the word

tall would correspond to a curve that defines the degree

to which any person is tall. If the set of tall people is

given the well-defined (crisp) boundary of a classical

set, we might say all people taller than 6 feet are

officially considered tall. But such a distinction is

clearly absurd. It may make sense to consider the set of

all real numbers greater than 6 because numbers belong

on an abstract plane, but when we want to talk about real

people, it is unreasonable to call one person short and

another one tall when they differ in height by the width

of a hair [31].

2.2.1. Fuzzy Logic Membership Functions used in

this Research

1. Trimf - Triangular-shaped built-in membership

function

Syntax: y = trimf(x, params)

y = trimf(x,[a b c])

Description: The triangular curve is a function of a

vector, x, and depends on three scalar parameters a, b,

and c, as given by

f (x;a,b,c) = max( min( , …… (3)

2.Gbellmf-Generalized bell-shaped built-in membership

function

Syntax:y = gbellmf(x,params)

Description:The generalized bell function depends on

three parameters a, b, and c as given by

f(x;a,b,c) = ……(4)

Where the parameter b is usually positive. The

parameter c locates the center of the curve. Enter the

parameter vector params, the second argument for

gbellmf, as the vector whose entries are a, b, and c,

respectively.

3. Trapmf-Trapezoidal-shaped built-in

membership function

Syntax: y = trapm f(x, [a b c d])

Description: The trapezoidal curve is a function of a

vector, x, and depends on four scalar parameters a, b, c,

and d, as given by

f(x;a,b,c,d)=max(min( ),0)………………(5)

The parameters aandd locate the “feet” of the trapezoid

and the parameters b and c locate the “shoulders.”

4. Gauss2mf - Two-sided Gaussian membership

function.

Syntax:y = gauss2mf(x,[sig1 c1 sig2 c2])

Description:TheGaussianfunctiondependsontwoparame

terssigandcasgivenby

f (x;σ,c) = ……….(6)

The function gauss2mf is a combination of two of the

setwoparameters. The first function,

specifiedbysig1andc1, determines the shape of the left-

mostcurve.

Thesecondfunctionspecifiedbysig2andc2determines the

shape of the right-most curve. Whenever c1 < c2,

thegauss2mf functionreachesamaximumvalueof1.

Otherwise,themaximumvalue islessthanone.

III. EXPERIMENTAL RESULTS

Experiments were done by taking original datafrom

NASA63 dataset [7]. The softwaredevelopment efforts

obtained when usingCOCOMO and other membership

functions wereobserved.

Figure 3.1: Output of the results in MATLAB


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Table 3.1:Developmental Effort Estimate using various Techniques

S.

No

Project

id

MODE SIZE EAF Actual

Effort

Int.

COCOMO

Est. Effort

Est.

Effort

using

Trap

MF

Est.

Effort

using

TMF

Est.

Effort

using

GBell

MF

Est.

Effort

using

Gauss2

MF

1 1 1.2 E 113 2.72 2040 2215.24 1920 1910 1790 1800

2 4 1.05 O 46 1.17 240 208.56 226 225 211 212

3 7 1.05 O 6.9 0.40 8 9.72 7.54 7.49 7.02 7.06

4 10 1.2 E 18 2.38 321 213.83 303 301 282 283

5 13 1.2 E 24 0.85 79 107.85 74.5 74 69.3 69.7

6 16 1.2 E 3.7 2.81 40 37.81 37.7 37.5 35.1 35.3

7 19 1.2 E 966 0.73 6600 7806.45 6220 6180 5790 5820

8 22 1.2 E 109 0.94 724 733.16 682 678 636 639

9 24 1.12 SD 90 0.70 453 324.32 427 424 398 400

10 28 1.05 O 13 2.81 98 132.89 92.3 91.8 86 86.5

11 31 1.2 E 50 3.14 1063 961.28 1003 996 933 938

12 34 1.2 E 22 1.76 230 201.18 218 215 202 203

13 35 1.2 E 13 2.63 82 160 78.2 76.8 72 72.3

14 40 1.05 O 2.5 0.96 8 8.04 7.54 7.49 7.02 7.06

15 43 1.05 O 28 0.96 83 101.61 78.2 77.7 72.9 73.2

16 46 1.05 O 57 0.74 126 165.21 119 118 111 111

17 49 1.12 SD 91 0.36 156 168.87 147 146 137 138

18 52 1.05 O 8.2 1.90 41 55.39 38.6 38.4 36 36.2

19 55 1.05 O 6.3 0.34 18 7.52 17 16.9 15.8 15.9

20 58 1.2 E 25 1.09 130 145.25 123 122 114 115

21 63 1.2 E 10 0.39 15 17.3 14.1 14.1 13.2 13.2

Table 3.2: Calculated MRE

MRE using Inter.

COCOMO Model

MRE using

TRAP MF

MRE using TMF MRE using GBell

MF

MRE using Gauss2

MF

0.0859 0.0588 0.0637 0.1225 0.1176

0.1310 0.0583 0.0625 0.1200 0.1166

0.2150 0.0575 0.0637 0.1225 0.1175

0.3339 0.0560 0.0623 0.1215 0.1184

0.3651 0.0570 0.0632 0.1228 0.1177

0.0547 0.0575 0.0625 0.1225 0.1175

0.1828 0.0575 0.0636 0.1227 0.1182

0.0126 0.0580 0.0635 0.1215 0.1174

0.2840 0.0573 0.0640 0.1214 0.1170

0.3560 0.0581 0.0632 0.1224 0.1173

0.0957 0.0564 0.0630 0.1223 0.1176

0.1253 0.0521 0.0652 0.1217 0.1174

0.9512 0.0463 0.0634 0.1220 0.1183

0.0050 0.0575 0.0637 0.1225 0.1175


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0.2242 0.0578 0.0638 0.1216 0.1180

0.3111 0.0555 0.0635 0.1190 0.1190

0.0825 0.0577 0.0641 0.1218 0.1154

0.3509 0.0585 0.0634 0.1219 0.1171

0.5822 0.0555 0.0611 0.1222 0.1166

0.1173 0.0538 0.0615 0.1230 0.1154

0.1533 0.0600 0.0600 0.1200 0.1200

Table 3.3: Computed MMRE

Developmental Model MMRE

Intermediate COCOMO 0.2373

FL Trapezoidal MF 0.0565

FL Triangular MF 0.0630

FL GBell MF 0.1218

FL Gauss2 MF 0.1175

Figure 3.2: Comparison of MMRE

0

0.05

0.1

0.15

0.2

0.25

Intermediate COCOMO

FL TRAP MF FL TMF FL GBell MF FL Gauss2 MF

DEVELOPMENTAL MODELS

MMRE

MMRE

IV. CONCLUSION AND FUTURE

RESEARCH

This research work is to provide a technique for

software cost estimation that performs better than other

techniques on the accuracy of effort estimation.

In this research an improved approach to software

project effort is projected by the use of fuzzy sets rather

than classical intervals in the COCOMO model. This

study explores four fuzzy logic membership functions:

Fuzzy Triangular Membership Function, GBell

Membership Function, Gauss2 Membership Function

and Trapezoidal Membership Function. Results shows

that the fuzzy logic can predict the more accurate results

than Classical Model (COCOMO). Also it can be easily

seen that the value of MMRE for Trapezoidal

Membership Function is the lowest. So Trap. MF is the

best among the four fuzzy logic functions used.

However if the transition between the phases is

smoothly required then the linear MF’s like Trapezoidal

and Triangular are not suitable. In that case it was found

that Gauss2 MF has lower value of MMRE than GBell

MF and hence is better.

The above research work can be analyzed in terms of

feasibility and acceptance in the industry.It can be

deployed on COCOMO II environment with experts

providing required information for developing fuzzy sets

and an appropriate rule base.

Future research involves that various techniques like

neural networks can also be used for Software effort

estimation [3]. Fuzzy logic techniques can also be

compared with other criterions like VAF, BRE, MARE,

Prediction %.

By applying some more effort there is the possibility to

develop other customized membership functions, which

represents inputs more closely to tolerate uncertainty

and imprecision in inputs, and hence restricting the same

to be propagated to the outputs.

REFERENCES

[1] A. R. Gray, S. G. MacDonell, “Applications of

Fuzzy Logic to Software Metric Modelsfor

Development EffortEstimation”,Fuzzy


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7

Information Processing Society 1997 NAFIPS

97, Annual Meeting of the North American, 21&

24 September 1997, pp. 394 & 399.

[2] A.C. Hodgkinson and P.W. Garratt, “A

NeuroFuzzy Cost Estimator”, in Proceedings of

the 3rd International Conference on Software

Engineering and Applications – SAE, pp. 401-

406, 1999.

[3] A.R. Venkatachalam, “Software cost estimation

using artificial neural networks”, Proceedings of

the 1993 International Joint Conference on

Neural Networks, pp. 987-990, 1993.

[4] AbouBakarNauman, Romana Aziz.,

“Development of Simple Effort Estimation

Model based on Fuzzy Logic using Bayesian

Networks”, IJCA Special Issue on “Artificial

Intelligence Techniques - Novel Approaches &

Practical Applications” AIT, 2011.

[5] Albrecht A.J., and J.E. Gaffney, “Software

function, source lines of code, and development

effort prediction: a software science validation,”

IEEE Transactions on Software Engineering, pp.

639-648, November1983.

[6] A. Idri, T. M. Khoshgoftaar, A. Abran. “Can

NeuralNetworks be Easily Interpreted in

Software CostEstimation”, IEEE Trans. Software

Engineering, 2002,pp. 1162 & 1167.

[7] B. W. Boehm, Software Engineering

Economics,Englewood Cliffs, NJ, Prentice Hall,

1981.

[8] B. W. Boehm, C. Abts and S.Chulani, “Software

Development Cost Estimation Approaches- A

Survey”, Technical Reports, University of

Southern California Centre for Software

Engineering, usccse 2000-505.

[9] Boetticher, G.D., “An assessment of metric

contribution in the construction of a neural

network-based effort estimator”, Proceedings of

Second International Workshop on Soft

Computing Applied to Software Engineering,

2001.

[10] GeetikaBatra and MahimaTrivedi, “A Fuzzy

Approach for Software Effort Estimation”,

International Journal on Cybernetics &

Informatics (IJCI), Vol.2, No.1, pp. 9-15,

February 2013.

[11] ImanAttarzadeh and Siew Hock Ow, “Software

Development Effort Estimation based on a New

Fuzzy Logic Model”, International Journal of

Computer Theory and Engineering, Vol. 1, No. 4,

October 2009.

[12] ImanAttarzadeh and Siew Hock Ow, “A Novel

Algorithmic Cost Estimation Model Based on

Soft Computing Technique”, Journal of

Computer Science 6 (2): ISSN 1549-3636 ©

2010 Science Publications, pp. 117-125, 2010.

[13] Jones C., “Estimating Software Costs”, McGraw-

Hill, 1998.

[14] L. H. Putnam, “A general empirical solution to

the macro software sizing and estimating

problem”. IEEE Transactions on Software

Engineering, SE-4(4),pp. 345-361, 1978.

[15] Lotfi A. Zadeh, “Fuzzy sets”,Information and

Control, Vol. 8, pp. 338–353, 1965.

[16] Lotfi A. Zadeh, “Fuzzy Algorithms”,Information

and Control, Vol. 12, pp. 94-102, 1968.

[17] Lotfi A. Zadeh, “Outline of a new approach to

the analysis of complex systems and decision

processes”, IEEE Trans. Systems, Man and

Cybernetics, Vol. 3, No. 1, pp. 28–44, 1973.

[18] Lotfi A. Zadeh, “Making Computers Think like

People”, IEEE Spectrum, 8, pp. 26- 32, 1984.

[19] Lotfi A. Zadeh, “Fuzzy Logic, Neural Networks

and Soft Computing”, Communication of ACM

37(3): pp. 77-84, 1994.

[20] Lofti A. Zadeh, “The Future of Soft Computing”,

In Joint 9th IFSA World Congress and 20th

NAFIPS International Conference, Vancouver,

Canada,2001.[21] Mamdani, E.H., “Advances in

the linguistic synthesis of fuzzy controllers,”

International Journal of Man-Machine Studies,

Vol. 8, pp. 669-678, 1976.

[22] Mamdani, E.H., “Applications of fuzzy logic to

approximate reasoning using linguistic

synthesis,” IEEE Transactions on Computers,

Vol. 26, No. 12, pp. 1182-1191, 1977.

[23] PankajJalote, “An Integrated Approach to

Software Engineering”, Third Edition, Narosa

Publishing House, 2006.

[24] Prasad Reddy, Sudha.K.R., Rama Sree P ,

Ramesh, “Fuzzy Based Approach for Predicting

Software Development Effort” International

Journal of Software Engineering (IJSE), Vol. 1,

No. 1, pp. 1-11,May 2010.

[25] Rahul Kumar Yadav,Dr. S. Niranjan , “Software

Effort Estimation Using Fuzzy Logic: A

Review”, International Journal of Engineering

Research & Technology (IJERT) Vol. 2, No. 5,

ISSN: 2278-0181,pp. 1377-1384, May 2013.

[26] Roger S Pressman, “Software Engineering-A

Practitioner’s Approach”, Tata McGraw-Hill

Edition 2010.

[27] RoheetBhatnagar, MrinalKanti Ghose, Vandana

Bhattacharjee, “Predicting the Early Stage

Software Development Effort using Mamdani

FIS”, RoheetBhatnagar et al, (IJCSIT)

International Journal of Computer Science and


________________________________________________________________________________________________

________________________________________________________________________________________________


8

Information Technologies, Vol. 2, No. 4, pp.

1675-1678, ISSN:0975 – 9646, 2011.

[28] RshmaChawla, Deepak Ahlawat, Mukesh

Kumar, “Software Development Effort

Estimation Techniques: A Review”, International

Journal of Electronics Communication and

Computer Engineering, Vol. 5, No. 5, ISSN

(Online):2249–071X, ISSN (Print): 2278–4209,

pp. 1166-1170,September 2014.

[29] RshmaChawla, Deepak Ahlawat, Mukesh

Kumar, “Improved Software Development Effort

Estimation Based on Fuzzy Logic Functions”,

International Journal of Engineering Sciences &

Research Technology, ISSN: 2277-9655,Vol. 3,

No. 12, pp. 529-535, December 2014.

[30] RshmaChawla, Deepak Ahlawat, “Improved

Software Development Effort Estimation Based

on Four Fuzzy Logic Functions”, International

Journal on Advanced Computer Theory and

Engineering (IJACTE), IRD India, ISSN (Print):

2319-2526, Vol. 4, No. 2, pp. 9-13, March 2015.

[31] The Math Works Inc., “Fuzzy logic toolbox- user

guide”, September 2010.

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