paper-6_enhanced fuzzy verdict mechanism for diabetes using fuzzy expert system

8/4/2019 Paper-6_Enhanced Fuzzy Verdict Mechanism for Diabetes using Fuzzy Expert System

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International Journal of Computational Intelligence and Information Security, August 2011 Vol. 2, No. 8

43

Enhanced Fuzzy Verdict Mechanism for Diabetes using Fuzzy Expert System

M.Kalpana[1]

and Dr. A.V Senthil Kumar[2]

[1]

Department of Physical Science and Information Technology,

Agricultural Engineering College and Research Institute,

Tamil Nadu Agricultural University, Coimbatore 641 003[2]

Department of MCA,

Hindusthan College of Arts & Science, Behind Nava India,

Coimbatore - 641028.

Email:[email protected] and [email protected]

Abstract

Fuzzy expert system can quantify the contribution of diabetes data with various parameters in terms of fuzzy

membership. By applying the enhanced fuzzy verdict mechanism the diagnosis of diabetes becomes simple for

medical practitioners. The enhanced fuzzy verdict mechanism consists of fuzzy inference, implication and

aggregation. The knowledge is constructed by using the fuzzification to convert crisp values into fuzzy values. This

mechanism, then assigns a triangular fuzzy numbers as aggregate measure of operations. Defuzzification method is

adopted to convert the fuzzy values into crisp values. In this paper a methodology, enhanced fuzzy verdictmechanism is proposed to complete the knowledge matrix that allows to obtain the rules of the system in simple and

quick way for diabetes data. The result of the proposed methods is compared with earlier method using accuracy as

metrics. The proposed enhanced fuzzy expert system is effectively hand crafted to achieve the desired

performance and also improves the accuracy of diabetes application.

Keywords: Fuzzy Expert System, Enhanced Fuzzy Verdict Mechanism, Fuzzification, Diabetes application.

1. Introduction

Campos-Delgado et al. [1] developed a fuzzy-based controller that incorporates expert knowledge by using

mamdani-type fuzzy logic controller to regulate the blood glucose level. Magni and Bellazzi [2] devised a stochastic

model to extract time course variability from a self-monitoring blood sugar level time series. The methodology

proposed is useful in variety of clinical contexts. Polat and Gunes [3] designed an expert system to diagnose the

diabetes disease based on principal component analysis which improves the diagnostic accuracy of diabetes disease.

Polat et al. [4] also developed a cascade learning system based on generalized discriminant analysis and least square

support vector machine to diagnose the diabetes. Chang and Lilly [5] developed an evolutionary approach to derive

a compact fuzzy classification system directly from data without any prior knowledge or assumptions on the

distribution of the data. Goncalves et al. [6] introduced an inverted hierarchical neuro-fuzzy BSP system for pattern

classification and rule extraction in databases. Kahramanli and Allahverdi [7] designed a hybrid neural network

system for classification of the diabetes database, aim of the classification is to increase the reliability of the result

obtained from the data. Chang-Shing Lee [8] designed as fuzzy expert system for diabetes decision support

application based on the fuzzy ontology with fuzzy decision making mechanism which simulates the semantic

description of medical staff for diabetes. Ismail saritas et al.[9] developed a fuzzy expert system to determine drug

dose in treatment of chronic interstine inflamation using the concept of fuzzification. The fuzzy expert system

designed can be applied in complex and uncertain fields such as the treatment of illness, to determine the exact dose

of medicine and evaluate clinic and laboratory data. Mehdi Fasanghari et al.[10] developed a fuzzy expert system

for Tehran stock exchange using the concept of fuzzification. The American Diabetes Association [11] categorizesdiabetes into type-1 diabetes, which is normally diagnosed in children and young adults, and type-2 diabetes, i.e., the

most common form of diabetes that originates from a progressive insulin secretory defect so that the body does not

produce adequate insulin or the insulin does not affect the cells. M. Kalpana and A. V Senthikumar [12] developed

fuzzy expert system using fuzzy verdict mechanism for diabetes application using the concept of fuzzification using

triangular membership function. Diabetes treatment focuses on controlling blood sugar levels to prevent various

symptoms and complications through medicine, diet and exercise.


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The increasing number of diabetics patients worldwide has drawn the attention to adopt some technologies such

as fuzzy expert systems and enhanced fuzzy verdict mechanisms for diabetes research. The proposed fuzzy expert

system gives the description for diabetes and support for the justification of the medical practitioners. The structure

of the rest of this paper is as follows: Section 2 deals with the architecture of fuzzy expert system. The experimental

results, implemented in MATLAB are presented in Section 3 and experimental results indicate that the proposed

fuzzy expert system can work more effectively than other methods can [3], [5], [7],[8],[12] in section 4.

2. Fuzzy Expert System for Diabetes ApplicationThis section describes a fuzzy expert system, including a Fuzzification, Enhanced Fuzzy verdict mechanism for

diabetes application and Defuzzification.

2.1 Pima Indians Diabetes DatabaseThe National Institute of Diabetes and Digestive and Kidney Diseases (NIDDK) [14] has examined the Pima

Indians Diabetes Database. This Database has one of the highest known rates of diabetes worldwide. The

experimental PIDD is retrieved from the Internet (http://archive.ics.uci.edu/ml/) and it contains the collected

personal data of the Pima Indian population. Table I lists the attributes of PIDD.Table I: Atttributes of PIDD

2.2 Architecture of the Fuzzy Expert System for Diabetes ApplicationFuzzy expert system is the notational representation of the process in terms of fuzzy variables, rules and

methods. Fuzzy concept is to transfer the information of the PIDD into the required knowledge. The fuzzy numbers

must be constructed according to the generated concepts. For the PIDD, each case has nine attributes, listed in Table

I, and each attribute can be constructed as a fuzzy variable with some fuzzy numbers. The relationship in the PIDD

with respect to age is given in Table II. The Architecture of the Fuzzy Expert System for diabetes application is

given in Figure 1.

Abbreviation Fullname Units

Pregnant Number of times pregnant -

Glucose Plasma glucose concentration in2-hours OGTT

mg/dl

DBP Diastolic blood pressure mmHg

TSFT Triceps skin fold thickness mm

INS 2-hour serum insulin mu U/ml

BMI Body mass index Kg/m2

DPF Diabetes pedigree function -

Age Age -

DM Diabetes Mellitus where 1 isinterpreted as tested positive

for diabetes

-


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Table II: Description of Fuzzy Relation

Figure 1:Architecture of the Fuzzy Expert System for diabetes application

2.3 Data PreparationThe data are taken from PIDD, the input variable are Plasma glucose concentration in 2-hours OGTT(Glucose),

2-hour serum insulin(INS), Body mass index(BMI), Diabetes pedigree function(DPF), Age(Age) and the output

Fuzzy Relation Description

REFU(Age0_25) Very Very Young

REFU(Age25_30) Very Young

REFU(Age30_35) More or Less Young

REFU(Age35_40) Slightly Young

REFU(Age40_45) Slightly Old

REFU(Age45_50) More or Less Old

REFU(Age50_55) Very Old

REFU(Age55_60) Very Very Old

FUZZIFICATION

INTERNET PIMA INDIAN

DIABETES

DATABASE(PIDD)

ENHANCED FUZZY VERDICT

MECHANISM FUZZY

RULES

BASE

DEFUZZIFICATION

CRISP

VALUE

DATA PREPARATION

Fuzzy Inference

,Implication and

A re ation


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variable are Diabetes Mellitus(DM). The data with the age group from 25-30 are taken to test the enhanced fuzzy

verdict mechanism.

2.4 FuzzificationFuzzification simply refers to the process of taking a crisp input value and transforming it into the degree

required by the terms[10]. If the form of uncertainty happens to arise because of imprecision, ambiguity, orvagueness, the variable is probably fuzzy and can be represented by a membership function.

In this stage input, output variables and their membership functions are defined. Next, based on the constructed

fuzzy concepts, the fuzzy numbers are built by the fuzzy relationship. Additionally, an interface is offered to tune

and validate the parameters of the built fuzzy numbers. In this paper a triangular function as shown in (1) is adopted

as the membership function of the fuzzy number and can be expressed as the parameter set[a,b,c]. The parameter is

fixed with Minimum value, Mean, Standard Deviation, Maximum value for each variable.Then the membership

function (x) of the triangular fuzzy number[13] is given by

( ) )1(

,0),/()(

),/()(

,0

>


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Figure 2: Membership graphics for the fuzzy three values Glucose

Figure 3: Membership graphics for the fuzzy values DM

2.5 Enhanced Fuzzy Verdict Mechanism

The Enhanced Fuzzy Verdict Mechanism separately infers the possibility of an individual developing diabetesfor each instance in fuzzification and transfers the possibility into the form of statement. According to the American

Diabetes Association [11], diabetes is associated with obesity, family history and age. Additionally, the American

Diabetes Association also indicates that the 2-hour OGTT with measurement of plasma glucose and serum insulin

concentrations are used as the criteria for diagnosing diabetes. Consequently, five attributes, i.e., Glucose, INS,

BMI, DPF and Age are selected as the input fuzzy variables of the adopted enhanced fuzzy verdict mechanism; in

addition, the related information about fuzzy numbers is stored in the fuzzification. The parameters of the fuzzy

numbers are listed in Table III and Table IV.


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Table III: Default constructed Fuzzy Numbers

Fuzzy

Numbers

Fuzzy

Numbers

Fuzzy triangular numbers

Glucose low Glucose[Min, Mean-SD, Mean]

medium Glucose [Mean-SD, Mean,

Mean+SD]high Glucose [Mean, Mean+SD, Max ]

INS low INS [Min, Mean-SD, Mean]

medium INS [Mean-SD, Mean, Mean+SD]

high INS [Mean, Mean+SD, Max ]

BMI low BMI [Min, Mean-SD, Mean]

medium BMI [Mean-SD, Mean,Mean+SD]

high BMI [Mean, Mean+SD, Max ]

DPF low DPF [Min, Mean-SD, Mean]

medium DPF [Mean-SD, Mean,Mean+SD]

high DPF [Mean, Mean+SD, Max ]

Age young Age [Min, Mean-SD, Mean]

medium Age [Mean-SD, Mean, Mean+SD]old Age [Mean, Mean+SD, Max ]

Table IV: Parameters of Triangular Membership Functions

Fuzzy

Numbers

Fuzzy

Numbers

Fuzzy triangular numbers

Glucose low [71 94.41 121.27]

medium [94.41 121.27 148.12]

high [121.27 148.12 196 ]

INS low [ 0 15.16 89.82]

medium [15.16 89.82 194.81]

high [89.82 194.81 579]

BMI low [ 0 24.46 33.24]

medium [24.46 33.24 42.03]

high [33.24 42.03 67.1]

DPF low [ 0.13 0.21 0.44]

medium [ 0.21 0.44 0.67]

high [ 0.44 0.67 0.96]

Age young [ 26 2627]

medium [26 27 29]

old [ 27 29 30]

DM verylow [0 0.1 0.2]

low [0.1524 0.2524 0.3]

medium [0.287 0.333 0.3997]

high [0.355 0.623 0.762]

veryhigh [0.731 0.831 1]

The fuzzy variable Glucosehas three fuzzy numbers, i.e., Glucoselow, Glucosemedium, and Glucosehigh. For

the fuzzy variable INS, fuzzy concepts and knowledge of the 2-hour serum insulin are expressed in human

communication by using the fuzzy numbers INSlow, INSmedium, and INShigh. The membership functions of BMI

also have three fuzzy numbers, i.e.,BMIlow,BMImedium, andBMIhigh. The fuzzy numbersDPFlow,DPFmedium,

and DPFhigh are defined for the fuzzy variable DPF. The membership functions of the fuzzy variable Age are


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Ageyoung, Agemedium, and Ageold. The five fuzzy numbers, i.e., DMverylow, DMlow, DMmedium, DMhigh, and

DMveryhigh, are adopted to represent the possibility of this instance with diabetes for output fuzzy variable DM.

The proposed Enhanced Fuzzy Verdict Mechanism consists of three steps, i.e., Fuzzy Inference, Implication

and Aggregation. Fuzzy Inference step is to take the fuzzified inputs and apply them to the antecedents of the fuzzy

rules. The developed fuzzy rule has multiple antecedents, the fuzzy operator OR is used to evaluate the rule

antecedents.Fuzzy interface is invoked by using Mamdanis approach On Implication is the process of mapping result of the

fuzzification from antecedent part into the consequence[18]. MIN operation is conducted by the system. The

implication process is conducted when the appropriate fuzzy rules are fired. More than one fuzzy rule fired at same

time. Implication results through the aggregation process.

The aggregation step combines the different consequent fuzzy sets into single fuzzy set. MAX operation is used

by the system. The membership degrees for all instances of the fuzzification are calculated. Enhanced Fuzzy Verdict

Mechanism analyzes the personal physical data, converts the inferred results into knowledge, and then presents the

decision results through descriptions [15], [16]. The patterns of the statement of the output descriptions, including a

statement analysis and a decision statement. Algorithm for the Enhanced Fuzzy Verdict Mechanism is given below.

Algorithm for Enhanced Fuzzy Verdict Mechanism

INPUTInput the fuzzy set for Glucose, INS, BMI, DPF and Age

OUTPUTOutput the fuzzy set for DM

METHODBegin

Step1:Input the crisp values for Glucose ,INS, BMI, DPF and Age.

Step 2: Calculate Glucose[Min, Mean-SD, Mean+SD, Max], INS[Min, Mean-SD, Mean+-SD, Max], BMI[Min,

Mean-SD, Mean+-SD, Max], DPF[Min, Mean-SD, Mean+-SD, Max] and

Age[Min, Mean-SD, Mean+-SD, Max].

Step 3: Set the triangular membership function for the fuzzy number with equation (1).

Step 4: Built the fuzzy numbers for Glucose, INS, BMI, DPF and Age for input set

Step 4.1: Built the fuzzy number for DM for the output set.

Step5: Fuzzy inference are executed by Mamdani s method.

Step 5.1: Input the rule as {Rule 1,2..n}

Step 5.2: Matching degree of rule with fuzzy OR operator are calculated for fuzzy input set (Glucoselow,Glucosemedium, Glucosehigh, INSlow, INSmedium, INShigh, BMIlow, BMImedium, BMIhigh, DPFlow,

DPFmedium, DPFhigh, Ageyoung, Agemedium, Ageold)

Step 5.3: Conduct Implication by MIN operation.

Step 5.4:Calculate the aggregation of the fired rules with MAX operation for fuzzy output set DM

(DMverylow, DMlow, DMmedium, DMhigh, DMveryhigh).

Step6: Defuzzify into the crisp values by

( )

( )

=

=

=ni

i

i

n

i

ii

i

Z

ZZ

DM

1

1

Where Zi means the weight for (Zi) and (Zi) means the number of fuzzy numbers of the output fuzzy variable

DM.Step6: Present the knowledge in the form of human nature language

End.

2.6 DefuzzificationDefuzzification process is conducted to convert aggregation result into crisp value for DM output. In this

process the single number which represent the outcome of the fuzzy set evaluation. The final combined fuzzy

conclusion is converted into a crisp value by using the centroid method.


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Statement pattern of output Descriptions

Statement Analysis(SA):The data exhibit that person is at [FNAge:young,medium,old]age, meanwhile the plasma glucose concentration in 2-

hour OGIT is [FNGlucose:low,medium,high], 2-hour serum insulin is [FNIINS:low,medium,high], body mass index is

[FNBMI:low,medium,high], and diabetes pedigree function is [FNDPF:low,medium,high]

Decision Statement(DS):The Decision statement justifies the possibility of suffering from diabetes for this person as

[FNDM:verylow,low,medium,high,veryhigh]

(Possibility:[0,1]).

3. Experimental Results

The proposed fuzzy expert system for diabetes application was implemented with the MATLAB. The

experimental environment was constructed to evaluate the performance of the proposed approach; in addition, PIDD

was chosen as the evaluated data set. The proposed approach can analyze the data of the PIDD and generate

corresponding human knowledge based on the Fuzzification for the parameter very young [8]. The first experiment

shows sets of results in Table V, indicating that the proposed approach automatically supports the analysis of the

data. The acquired information is then transferred into knowledge, and finally the proposed method presents them in

the form of the descriptions of humans.

Rule for Fuzzy Expert System

1. If(Glucose is Glucoselow) or(INS is INSlow) or (BMI is BMIlow) or (DPF is DPFlow) or(Age is Ageyoung)isDMverylow

2. If(Glucose is Glucoselow) or(INS is INSlow) or (BMI is BMIhigh) or (DPF is DPFlow) or(Age is Ageyoung)then (DM is DMlow)

3. If(Glucose is Glucosemedium) or(INS isINShigh) or (BMI is BMIhigh) or (DPF is DPFmedium) or(Age isAgeyoung) then (DM is DMmedium)

4. If(Glucose is Glucosehigh) or(INS is INSmedium) or (BMI is BMIhigh) or (DPF is DPFhigh) or(Age isAgeyoung) then (DM is DMhigh)

5. If(Glucose is Glucoselow) or(INS is INSlow) or (BMI is BMImedium) or (DPF is DPFlow) or(Age isAgeyoung) then (DM is DMverylow)


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Table V: Result obtained from MATLAB

4. Evaluation of System PerformanceThe second experiment evaluates the performance of the Decision statement and the medical practitioner.

Accuracy is the measuring scale for performance of this experiment. The True Positive (TP) and the True Negative

(TN) denote the correct classification. False Positive (FP) is the outcome when the predicted class is yes (or

positive) and actual class is no (or negative). Still, a False Negative (FN) is the outcome when the predicted class is

no (or negative) and actual class is yes (or positive). Table VI lists the various outcomes of a two-class prediction

[17]. Accuracy is the proportion of the total number of predictions that were correct. The precision is the proportion

of the predicted positive cases that were correct. The eqn. (3) show the formula for accuracy.

Table VI

Data Glucose(mg/dl)

INS(mu

U/ml)

BMI(Kg/

m2)

DPF Age

146 194 38.2 0.329 29

SA If(Glucose is Glucosehigh) or(INS is INSmedium) or (BMI is

BMIhigh) or (DPF is DPFhigh) or(Age is Ageyoung) then (DM is

DMhigh)

DS The Decision statement justifies that the possibility of suffering

from diabetes for this person is medium(possibility:0.406)

Justification

by Medical

Practitioner

Medical practitioner justification is the person is diabetes

)3(%100 +++

+

= XTPFNFPTN

TPTNAccuracy


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Table VII: Comparison of Proposed method

Accuracy with earlier methods

The final experiment compares the accuracy of the proposed method with results of studies involving the PIDD [5],

[6], [8][12]. Comparing these methods, as listed in Table VII, reveals that the proposed method achieves the first

highest accuracy values for very young based on the proposed fuzzy expert system. The accuracy values of the

proposed method are compared with the earlier methods and represented graphically figure 4, which shows better

accuracy.

Figure 4: Graphical represent of accuracy

MethodAccuracy

(%)Author

Our study for Very Young 87.38 M.Kalpana and Dr. A.V.Senthil Kumar

FES for diabetes using Fuzzy verdictMechanism

85.03 M.Kalpana and Dr. A.V.Senthil Kumar

A FES for Diabetes Decision very young[8] 81.7 Lee and Wang

HNFB-1[6] 78.26 Goncalves et al.

Logdisc 77.7 Statlog

IncNet 77.6 Norbert Jankowski

DIPOL 92 77.6 Statlog

Linear discr. Anal 77.5-77.2 Statlog, ster and Dobnikar

A FES for Diabetes Decision very very

young[8]

77.3 Lee and Wang

VISIT[5] 77 Chang and Lilly

SMART 76.8 statlog

GTO DT(5 X CV) 76.8 Bennet and Blue

ASI 76.6 Ster and Dobnikar

Fisher discr. Analysis 76.5 Ster and DobnikaMLP+BP 76.4 Ster and Dobnika

LVQ(20) 75.8 Ster and Dobnika

LFC 75.8 Ster and Dobnika


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5. Conclusions and Future ResearchThis paper presents fuzzy expert system for diabetes using enhanced fuzzy verdict mechanism. The

experimental data set, PIDD, is initially processed and the crisp values are converted into fuzzy values in the stage

of fuzzification. The enhanced fuzzy verdict mechanism undergoes three steps to executes rules, to make a decision

on the possibility of individuals suffering from diabetes and to present the knowledge with descriptions.

Defuzzification process is conducted to convert the result into crisp value for Diabetes Mellitus output.Experimental results indicate that the proposed method can analyze data and further transfer the acquired

information into the knowledge to simulate the thinking process of humans. The results further demonstrate that the

proposed method works more effectively for diabetes application than previously developed ones. Future works

should test the fuzzification approach used herein for other similar tasks or other related data sets to evaluate its

capability to produce a similar accuracy. Future works should undertake the composition and add more rules to

improve the accuracy of Enhanced Fuzzy Verdict Mechanism.

References[1] D. U. Campos-Delgado, M. Hernandez- Ordonez, R. Femat, and A. Gordillo-Moscoso, (2006) Fuzzy-based

controller for glucose regulation in type-1 diabetic patients by subcutaneous route,IEEE Trans. Biomed.Eng.,

vol. 53, no. 11, pp. 22012210.

[2] P. Magni and R. Bellazzi, (2006)A stochastic model to assess the variability of blood glucose time series in

diabetic patients self-monitoring,IEEE Trans. Biomed. Eng., vol. 53, no. 6, pp. 977985.

[3] K. Polat and S. Gunes, (2007) An expert system approach based on principal component analysis and

adaptive neuro-fuzzy inference system to diagnosis of diabetes disease, Dig. Signal Process., vol. 17, no. 4,

pp. 702710.

[4] K. Polat, S. Gunes, and A. Arslan, (2008) A cascade learning system for classification of diabetes disease:

Generalized discriminant analysis and least square support vector machine, Expert Syst. Appl., vol. 34, no. 1,

pp. 482487.

[5] X. Chang and J. H. Lilly, (2004 )Evolutionary design of a fuzzy classifier from data,IEEE Trans. Syst., Man,

Cybern. B, Cybern., vol. 34, no. 4, pp. 18941906.

[6] L. B. Goncalves, M. M. B. R. Vellasco, M. A. C. Pacheco, and F. J. de Souza, (2006) Inverted hierarchical

neuro-fuzzy BSP system: A novel neuro-fuzzy model for pattern classification and rule extraction in

databases,IEEE Trans. Syst., Man, Cybern. C, Appl. Rev., vol. 36, no. 2, pp. 236248.

[7] H. Kahramanli and N. Allahverdi, (2008 )Design of a hybrid system for the diabetes and heart diseases,

Expert Syst. Appl., vol. 35, no. 1/2, pp. 8289.

[8] Chang-Shing Lee, (2011) A Fuzzy Expert System for Diabetes Decision Support Application IEEE

transactions on systems, man, and cyberneticspart b: cybernetics, vol. 41, no. 1.

[9] Ismail Saritas Ilker A. Ozkan Novruz Allahverdi Mustafa Argindogan, (2009) Determination of the drug

dose by fuzzy expert system in treatment of chronic intestine inflammation Springer Science+Business Media

J Intell Manuf 20 PP 169176.

[10] Mehdi Fasanghari, Gholam Ali Montazer,( 2010) Design and implementation of fuzzy expert system for

Tehran Stock Exchange portfolio recommendationExpert Systems with Applications 37 PP 61386147.

[11] American Diabetes Association, Standards of medical care in diabetes2007, Diabetes Care, vol. 30, no.

1, pp. S4S41.

[12] M.Kalpana and A.V Senthilkumar,(2011)Fuzzy Expert System for Diabetes using Fuzzy Verdict Mechanism

International Journal of Advanced Networking and Applications (onprint)

[13] William Siler and James Buckley,( 2005)Fuzzy Expert System and Fuzzy Reasoning Wiley & Sons,Inc pp,49-50.

[14] J. Demouy, J. Chamberlain, M. Harris, and L. H. Marchand, (1995) The Pima Indians: Pathfinders of Health.

Bethesda, MD: Nat. Inst. Diabetes Digestive Kidney Diseases.

[15] L. A. Zadeh, (2008) Toward human level machine intelligenceIs it achievable? The need for a paradigm

shift,IEEE Comput. Intell. Mag., vol. 3, no. 3, pp. 1122.

[16] M. Margaliot,( 2008) Biomimicry and fuzzy modeling: A match made in heaven, IEEE Comput. Intell.

Mag., vol. 3, no. 3, pp. 3848.


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[17] C. S. Lee and M. H. Wang,( 2007) Ontology-based intelligent healthcare agent and its application to

respiratory waveform recognition,Expert Syst.Appl., vol. 33, no. 3, pp. 606619.

[18] Arazi Idrus, Muhd fadhil Nuruddin, M. arif Rohman, (2011)Development of project cost contingency

estimation model using risk analysis and fuzzy expert system , Expert System with applications

38(2011) 1501-1508.

paper-6_enhanced fuzzy verdict mechanism for diabetes using fuzzy expert system

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