the fuzzy cooperative genetic algorithm (fcoga): the optimisation of a fuzzy model through...

8/3/2019 The fuzzy cooperative genetic algorithm (FCoGA): The optimisation of a fuzzy model through incorporation of a cooperative coevolutionary method

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The fuzzy cooperative genetic algorithm(FCoGA): The optimisation of a fuzzy model

through incorporation of a cooperative

coevolutionary methodArfian M. Ismail, Hishammuddin Asmuni, and Razib M. Othman

Abstract — Genetic Algorithms (GA) have been widely used to represent parameters in a fuzzy system. However, when a fuzzy

system is applied to a complex problem, GA tends to lose their effectiveness because of the representation complexity of the

solution. In this paper, an improved method of fuzzy modelling called as Fuzzy Cooperative Genetic Algorithm (FCoGA) is

introduced. Cooperative Coevolution (CC) is applied to the GA by subdividing the chromosome into three sub-chromosomes

known as species, and thus reducing the representation complexity of the solution. Furthermore, two-level evaluations in the

FCoGA, at the species level and cooperative chromosome level, are introduced to improve the performance. To measure the

performance of FCoGA, two benchmark datasets namely Wisconsin Breast Cancer Diagnosis (WBCD) and Pima Indian

Diabetes (PID) datasets have been used. The experimental results show that FCoGA slightly improves the accuracy rate and

maintains comparable effectiveness with other existing study solutions.

Index Terms — Cooperative coevolutionary algorithm, Genetic algorithm, Cooperative chromosome, Fuzzy modelling.

—————————— ——————————

1 INTRODUCTION

fuzzy system gives reasons for its results because ithas the ability to give explanations using fuzzy rulesand membership functions, and modelled the out-

put from a given inputs [35,37]. To obtain the output,fuzzy systems work by implementing fuzzy logic andapproximate reasoning, and then incorporating themwith expert knowledge before apply it in the inferencesystem [44]. Fuzzy system has an ability to extract andinterpret the knowledge that is contained in the data [6,16, 35]. In addition, it also can handle uncertain and im-precise knowledge in real-world applications, and dealwith vagueness, noisy, inaccurate and incomplete data[42]. Currently, fuzzy systems have been successfully ap-plied in many fields, such as engineering [29, 33, 45],medicine [13, 14, 41] and the food industry [3, 31, 38].When developing a fuzzy system, several parametersmust be identified in order to obtain the desired beha-viour of the system [35]. This process is known as fuzzymodelling [8]. The objective of modelling a fuzzy systemis to develop reliable and understandable models for hu-

man beings.Current researches in fuzzy modelling have focus in

defining the fuzzy system parameters by automated the

process of generating and tuning fuzzy rule and member-ship function for optimisation. Most of the work com-bines a fuzzy system with an evolutionary method, GA,which utilises learning capabilities to solve complex prob-lems [11, 12, 19, 20, 23, 24, 27, 36, 50]. GA can be viewedas a search technique where the goal is to find the optimal(or close approximate to the optimal) solution to thesearch problem. GA involves mechanisms inspired bybiological evolution: selection, crossover and mutation.Generally, the solution of GA is represented by the com-bination of bit strings, known as chromosomes. Theprocess of GA starts with a random population that isgenerated and continues until a termination condition isreached. For every generation, the fitness of all chromo-somes is evaluated and selected to be modified (by per-forming crossover and mutation operations) to produce anew generation. Work that involves the generationprocess of fuzzy rules by GA has been performed by Liand Wang [23]. They propose niching methods to gener-ate fuzzy rules, and GA is then used to fine tune and im-

prove the quality of the fuzzy rules. Li et al. [24] introduc-es Fuzzy Feature Extraction Agent (FFEA) and FuzzyClassification Unit (FCU) to automatically generate andtune fuzzy rules by applying GA and Adaptive GradeMechanism (AGM). Evsukoff et al. [12] used GA to adjustand tune fuzzy rules to improve classifier performanceand reduce model complexity. Similar with Zhang et al. [50] work’s where they also used GA to improve thefuzzy rule. They proposed a new approach that uses GAto represent the fuzzy rule in three separate species. Their

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A. M. Ismail is with the Universiti Teknologi Malaysia, 81310 UTM Sku-dai, Malaysia.

H. Asmuni. is with the Universiti Teknologi Malaysia, 81310 UTM Sku-dai, Malaysia.

R. M. Othman is with the Universiti Teknologi Malaysia, 81310 UTM Skudai, Malaysia.

A

© 2011 Journal of Computing Press, NY, USA, ISSN 2151-9617

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Fig.3. Encoding process of S FR .

V and CL= linguistic variable (attribute of data) A and C = linguistic value (value of data) n = no. of attribute

r = no of rule

IF (V 1

r IS A1

r ) AND ( V 2

r IS A2

r ) AND …… ( V n

r IS An

r ) THEN ( CLr IS C r ) Encode process

A1

r A2

r … An

r C

r

V 1r V 2

r … V n

r CL

r

fuzzy rule in an IF-THEN form:

IF (V 1i IS A1 i) AND ..(V j i IS A j i) THEN (CLASSi IS Ci)

where V is the linguistic variable (an attribute of the data)and A is the linguistic value (a value of the data). Thesymbol j denotes the number of attributes contained inthe data and i is the number of the fuzzy rules. Theprocess of encoding SFR can be seen in Fig. 3. The lengthof SFR is dependent on the number of fuzzy rules and thenumber of antecedents involved in each rule.

The second species, S MF , holds all the starting points ofthe membership functions that define for the fuzzy sys-tem (represented by P in Fig. 4(a)). The starting point foreach membership function is encoded in a numericalformat. In this study, the membership function used istrapezoidal in shape, as shown in Fig. 4(a). The example

of the encoding process of S MF is illustrated in Fig. 4(c).The value of every gene in S MF (P1,P2,Pn and PCL)represents the starting point of the overlap in the mem-bership function that is taken from P in Fig. 4(b), and theirlength (S MF ) depends on the number of attributes in itsparticular dataset.

The last species, SRG, determines the overlap length inthe membership functions for all linguistic variables. SRG is also encoded in a numerical format and the length ofSRG is the same as the length of S MF . Fig. 4 shows the en-coding process of SRG. For each linguistic variable, theoverlap length in the membership functions is

represented by d as shown in Fig. 4(a). The value of genesin SRG as shown in Fig. 4(c), represent the overlap lengthsfor the input linguistic variables (V 1 to V n) and the outputlinguistic variable (CL).

2.2 Fitness Evaluation

The fitness function is used to evaluate the quality of thesolution. In this method, two levels of fitness evaluationare used: the fitness evaluation at the species level,known as the species fitness function, and the fitnessevaluation at the cooperative chromosome level, knownas the cooperative chromosome fitness function. The rea-son for the introduction of these two levels of fitnessevaluation is to ensure that the highest quality solutionsare discovered. This can be achieved by allowing the spe-cies with the highest fitness value to be chosen first to

cooperate with others to become the cooperative chromo-some. By doing this, the solution with highest quality canbe produced. In addition, this also speeds up the learningprocess in FCoGA. The species fitness function is appliedto all species except the SRG, whereas the cooperativechromosome fitness function can be performed when allspecies have been combined to assemble a complete solu-tion of the fuzzy model.

Before the complete of the fuzzy model is achieved, thespecies must be measured to determine their quality. Atthis stage, a pair from each species is selected to represent

1 BEGIN FCoGA

2 g:=0

3 j:={SFR ,S MF ,SRG}

4 FOR all j

5 initialize population SP j g

// SP j g is species of chromosome

6 choose rep_ SP j g from SP j g

7 END‐FOR

8 assemble CM g by combine all rep_ SP j g

//CM is complete model

9

evaluate CM g

10 WHILE NOT termination‐condition DO

11 j:={SFR ,S MF ,SRG}

12 FOR all j

13 g:= g +1

14 elite_selecti g from SP j(g‐1)

15 select SP j g from SP j(g‐1)

16 crossover SP j g

17 mutate SP j g

18 new_ SP j g by combine elite_selecti g with SP j g

19 evaluate new_ SP j g

20 choose rep_ SP j g from new_ SP j g

21 END‐FOR

22 assemble CM g by combine all rep_ SP j g

23

evaluate CM g

24 END‐WHILE

25 RETURN the best of model

26 END FCoGA

Fig. 1. Pseudo-code of the FCoGA.

Fig. 2. Overview of species in the FCoGA.






their species in assembling the complete fuzzy model.The pair from each species that is selected is also knownas the species’ representatives. The fitness function of theSFR can be stated as follows:

-FR maxFR fitt = acc v (1)

where acc is the correct case diagnosis percentage (classi-fication performance) and vmaxFR refers to the maximumnumber of variables in the longest rule. The purpose ofvmaxFR is to measure the interpretability of the rule, wherethe fuzzy rules with large variables are penalised to guar-antee that simple rules with fewer variables are applied[10, 35]. The fitness function of the S MF can be formulatedas follows:

MF MF fitt acc n (2)where n MF is the number of applied membership func-tions. The correct case diagnosis percentage is subtractedfrom the number of membership functions to discover the

species with the highest fitness. This is done so that whenthe number of membership functions increases, the fit-ness value decreases and the fuzzy model becomes lessclosely interpreted [48].

For the SRG, the fitness function is not applied. Theprocess of selecting a pair of individuals is accomplishedby a random function and that keeps the exploration ofthe search space at a minimum [35, 47]. Besides that, thereis no criterion to be measured in the overlap length in themembership functions.

After each species has been selected, the representa-tives are assembled to perform within the fuzzy model.At this stage, the combination of all representatives is

known as the cooperative chromosome. The following isthe formula of cooperative chromosome fitness:

( )cc cerr MF maxFR fit acc n n v (3)where ncerr is the number of classification errors in thedata. The cooperative chromosome covers two criteria,which are the achievement of truly classified values (clas-sification performance) and the interpretability of thefuzzy model that is gained from fitFR and fit MF . The prac-tical fuzzy model can be considered when there are fewervariables in the rules and the maximum number of rulesis limited to ten [48]. The fuzzy model becomes less inter-pretable and loses its resemblance to human intelligencewhen the number of rules increases [30, 43, 48].

2.3 Classification of Fuzzy Systems

Generally, fuzzy systems consist of four components: theknowledge base, the fuzzifier, the inference engine andthe defuzzifier. In this study, the knowledge base is com-prised of rules and membership functions, whereas thefuzzifier is a mechanism to translate the crisp input (data)

into the fuzzy input. The inference engine is a reasoningprocess for making use of the fuzzy operator to obtain thefuzzy output. The inference engine used in this study is aSazonov [39] fuzzy engine that can be downloaded fromhttp://people.clarkson.edu/~esazonov. The defuzzifieris the method that translates the fuzzy output back intocrisp output.

2.4 Selection

Selection is the process of selecting the species on whichthe reproduction process is executed. For SFR and S MF ,tournament selection is used to obtain the best speciesbased on their fitness. This is to enable the ‘best’ of SFR

and S MF to be selected first to bring about the reproduc-tion. Meanwhile, for the SRG, a random function is usedfor the selection process. This is to maintain explorationof the search space that is performed by GA [35, 47]. Inaddition to the conventional means of selection, thisstudy incorporates the concept of elitism (elite selection),where an Erate rate is used to allow some of the best spe-cies from previous generations to survive through to thenext generation. The concept of elitism, depicted in Fig. 5,helps avoid varying behaviour among species popula-tions [35, 48], and subsequently, maintains the geneticinformation of the best species discovered by the evolu-tion process. Therefore, elitism allows high quality solu-tions to be found within a smaller number of generations.

Population g+1

Population g

Elitist

Some of species in

pervious generation

are selected with

probability E rate rate.

Fig. 8. Concept of elite selection.

Before applied elite

selection

After applied elite

selection

Fig. 4. Encoding process of S MF and S RG .

P d

Low High

1

0 Value

Degree of membership function

(a) Schematic of membership function for V 1.

P 1 P 2 … P n P CL

V 1r V 2

r V n

r CL

r

(b) Encoding process of S MF .

(c) Encoding process of S RG .

d 1 d 2 … d n d CL

V 1r

V 2r

V nr

CLr

Fig. 5. Concept of elite selection.






2.5 Reproduction

Reproduction is the process of creating a new generation(children) of a species by crossover and/or mutationprocesses on the previous generation (parents). The re-production process only happens within the same spe-cies. The purpose of reproduction is to discover the bestcombination of fuzzy models by producing subsequent

generations.In the crossover process, a two-point crossover is per-formed on the SFR, whereas a one-point crossover is doneon the S MF and SRG species. The two-point crossover isapplied to SFR because of a rule that has two parts: input(attribute of data) and output (class of data). On the otherhand, a one-point crossover is completed for S MF and SRG to prevent the new offspring’s features being differentfrom its parents. The crossover between species is per-formed with a probability of pc. The point of crossover ischosen by a random function on the parent. An exchang-ing process then takes place to produce two newoffspring. If no crossover takes place ( pc is equal to 0), thenew offspring will become exact copies of their parents

(unless mutation takes place).The rationale for mutation in this method is to create

slight diversity within the population by changing a val-ue of a gene. In this method, mutation is performed bymutating a gene from a species with a probability of pm. If

pm is equal to 0, mutation will not take place. The point formutation is searched for by a random function.

3 EXPERIMENTAL SETUP

To evaluate the proposed method, two well-known data-sets for evaluating fuzzy systems are used: WisconsinBreast Cancer Diagnosis (WBCD) and Pima Indian Di-

abetes (PID). These datasets were obtained from the Uni-versity of California, Irvine (UCI) machine learning repo-sitory. First a brief explanation of each dataset used ispresent, followed by a description of the dataset withinthe context of the experiment. Finally, the results of theFCoGA are presented.

3.1 Dataset Description

3.1.1 Wisconsin Breast Cancer Diagnosis (WBCD)Dataset

The WBCD dataset has been widely used to evaluate theperformance of classifier systems such as the geneticfuzzy system [35], neural networks [40], support vector

machines [2] and decision trees [1]. The WBCD dataset isused to differentiate the diagnoses of cases between be-nign and malignant. The WBCD dataset contains nineattributes and one output with 699 diagnosis cases inwhich 458 are benign samples and the rest are malignant.However, 16 cases are reported incomplete and thereforeomitted in this experiment [40]. As a result, only 683 di-agnosis cases are used in which 444 cases are benign and239 cases are malignant. The attributes are clump thickness (v1), uniformity of cell size (v2), uniformity of cell shape (v3),

marginal adhesion (v4), single epithelial cell size (v5), bare nuc-lei (v6), bland chromatin (v7 ), normal nuclei (v8) and mitosis (v9), and one diagnosis case of cancer (either benign or ma-lignant). The data are divided into nine categories of input(v1 to v9) and one output (benign or malignant).

3.1.2 Pima Indian Diabetes (PID) Dataset

Besides the WBCD dataset, FCoGA was also tested on the

PID dataset. This dataset has been used by many studies[9, 12, 14, 18, 20]. All data in this dataset comes from PimaIndian women who are at least 21 years of age and livingnear Phoenix, Arizona, USA. This dataset consists of 768data that comprise eight attributes and one output. Theattributes are number of times pregnant (v1), plasma glucoseconcentration a 2 h in an oral glucose tolerance test (v2), dias-tolic blood pressure (v3), triceps skin fold thickness (v4), twohour serum insulin (v5), body mass index (v6), pedigree func-tion (v7 ) and age (v8). The value of the output (v9) class is 0(negative test) or 1 ( positive test). There are 500 (65.1%) cas-es in class 0 and 268 (34.9%) cases in class 1.

3.2 Experimental EnvironmentThe experiment of this study involves several parametersettings, the purpose of which is to discover the best suiteof parameters to obtain the best possible results. Table 1shows the parameter settings involved in this experiment.Because of the nature of CCA, which breaks the problemsto sub-problems, a small population with sizes rangingfrom 30 to 70 chromosomes is preferred in FCoGA. Theprobability of crossover and mutation is tested in therange of 0.5 to 1.0 for crossover and 0.0 to 0.5 for mutationto find the best combination between them. This is in linewith the current research trends, which posit that betterresults will be produced when the crossover probability

approaches 1 and the mutation probability goes to 0 [10,15, 17, 19, 23, 33, 34, 48]. The number of generation de-pends on the number of rule; where the number of rule ismultiplied by 100. The number of rules is fixed at 10: witha greater number of rules, the fuzzies become less inter-pretable and loses its resemblance to human intelligence[30, 43, 48]. The method is tested with a program writtenin JAVA and employing an inference engine. This expe-riment has been conducted by using a 10-fold cross vali-dation, where the data is partitioned into 10 equal sizesand the process of running the experiment is repeated 10times on every portion of data. The effectiveness of FCo-GA is validated using the percentage of correctly pre-dicted cases produced by FCoGA. The percentage of ac-

curacy can be determined by (4):

( ) / 100 Accuracy (acc) TP TN no. of data (4)where TP is true positive (the number of cases A is cor-rectly predicted as A), whereas TN is true negative (thenumber of cases B is correctly predicted as B) and no. ofdata is the number of data that has been tested. The accu-racy chosen is validated by other existing studies thathave used accuracy in the validation of their techniques[13, 14, 18, 20, 25, 35, 42].






3.3 Experimental Results

The results obtained by FCoGA when applied on theWBCD and the PID Indian datasets are showed in Table2. The best parameter setup is shown in Table 3, whereboth of the datasets use same setting to produce the ‘best’result. From the experiment on the WBCD dataset, thehighest average accuracy is 98.42% with the number ofrule is 10; the best is 100% when the number of rule istwo; while the worst is 82.37% when the number of rule is

10. For evaluation purposes, the FCoGA performance iscompare with other techniques as illustrated in Table 4,which shows that FCoGA obtained the highest accuracyof all techniques. For the experiment performed on thePID dataset, the highest average accuracy obtained is78.17% when the number of rule is 10; the best is 84.42%when the number of rule is three; and the worst is 65.79%when the number of rule is 10. To evaluate the perfor-mance of FCoGA, Table 5 shows the comparison withother techniques when applied on the PID dataset. Itshows that FCoGA achieves the highest average accuracywhen compared to other techniques.

4 DISCUSSION The main objective of this study is to propose an im-proved fuzzy modelling method that can obtain classifi-cation accuracies that are better than those of existing me-thods. In addition, the interpretability of the fuzzy system

also needs to be considered. Although there is no stan-dard definition of interpretability for a fuzzy system, sev-eral studies have defined interpretability as covering cer-tain factors; for instance, the characteristics of the fuzzyrules, where only a few membership functions (attributesof data) are applied [30, 43, 48]. Moreover, another studyhas defined the interpretability of a fuzzy system by thenumber of rules [23, 33]. Mencar and Fanelli [28] statedthat the interpretability of the model must take into con-sideration whether it can be reasonably understood by

humans. Therefore, the FCoGA has been designed to setthe new standard in classification accuracy while retain-ing (or improving) interpretability. Using the best para-meter setup for the experiments (Table 4), the FCoGA hasobtained the highest accuracy and only needs a smallnumber of rules. In addition, these rules use only a fewmembership functions. Fig. 6 shows the ‘best’ model ob-tained by the FCoGA when applied to a WBCD. Thismodel applied only two rules: there are four membershipfunctions in the longer rule and only one membershipfunction in the shorter rule. This set of fuzzy rules em-ployed only five membership functions in total. Mean-while, Fig. 7 shows the ‘best’ model when the FCoGA isapplied to PID dataset. This model also utilised two fuzzyrules, with five membership functions in the longer ruleand only one membership function in the shorter rule.The fuzzy rules in this model applied a total of six mem-bership functions.

TABLE 1PARAMETER SETTINGS

Parameter Value

Population size [30, 70]Crossover probability [0.5, 1.0]Mutation probability [0.0, 0.5]Elite probability [0.1, 0.5]

No. of rules [1, 10]Generation 100 × no. of rules

TABLE 3THE BEST PARAMETER SETTING ON WBCD AND PIMA

DATASETS

Parameter Value

Population size 50

Crossover probability 0.9

Mutation probability 0.3

Elite probability 0.1

No. of rules 10

TABLE 2THE RESULTS OF WBCD AND PID DATASETS

No. of rulesWBCD dataset (%) PIMA dataset (%)

Average Best Worst Average Best Worst

1 59.17 76.47 0.00 44.85 61.04 18.18

2 76.73 100.00 60.29 53.14 68.83 18.18

3 88.72 100.00 60.29 74.01 85.72 58.44

4 92.22 100.00 67.65 73.89 81.82 40.26

5 95.71 100.00 70.59 73.10 81.82 44.16

6 95.75 100.00 57.35 71.66 84.42 57.89

7 97.14 100.00 60.92 74.79 81.82 59.21

8 96.83 100.00 51.47 72.72 84.82 44.16

9 96.45 100.00 69.12 76.09 81.82 63.64

10 98.42 100.00 82.35 78.17 84.42 65.79






From the experiments that were tested on the WBCDand the PID datasets, FCoGA obtained the highest aver-age of accuracy when it is compared to other works. Thesuccessfulness of FCoGA in producing the highest classi-fication accuracy may have been contributed by the twofitness levels of evaluation which are at the species leveland at the cooperative chromosome level. This is becauseall of the species with the highest fitness value collabo-rates with each other to perform the completion solution.By doing this, the quality of the complete solution can befound easier and able to produce the fuzzy model thatcan achieve higher classification accuracy. To support thisstatement, Table 6 shows the comparison of FCoGA withone level fitness evaluation and FCoGA with two levelfitness evaluations. FCoGA with one level fitness evalua-tion refers to the fitness evaluation that only occurs at thecooperative chromosome level and the species selected toperform the cooperative chromosome is chosen by ran-dom function.

The concept of cooperative chromosomes has beenadopted in this study to simplify the representation of thesolution. As a consequence, the learning process of FCo-GA is rapid. This might have been because of the processof breaking the problems into sub-problems. Fig. 8 andFig 9 show the graph of the fitness per generation by us-ing the best set of parameter settings (Table 3) to show thespeed of learning. Fig. 8 shows the FCoGA applied to theWBCD dataset. The most rapid learning process in allexperiments can be considered to be from the 0th to 15thgenerations, in which the graph shows that fitness issharply improved, and needs only 15 generations to learnthe problem. Furthermore, the improvement in all expe-riments that occurred from the 0th to 15th generation canbe considered to be at an earlier generation. In Fig. 9, thegraph shows the fitness of FCoGA when applied to thePID dataset. From the graph, it can be seen that from gen-eration 0th to 5th, the fitness in all experiments improved

sharply. With regards to the beginning of the learningprocess, this can be considered as the most rapid learning,taking only five generations to learn the problem beforestabilising. Also, the learning process that began betweenthe 0th and 5th generations can be considered at earliergenerations. Because of the rapid learning process ofFCoGA, the maximum numbers of generations neededare only 190 and 200 for the WBCD and PID datasets, re-spectively. Compared to the decomposed method, theFCoGA with single species was also tested. Single speciesmeans that the FCoGA has only one species thatrepresents the solution. Fig. 10 and Fig. 11 plotted the line

TABLE 4COMPARATIVE RESULTS OF WBCD DATASET WITH OTHER

TECHNIQUES

Technique by Accuracy (%)

Li and Wang [23] 96.09

Gadaras and Mikhailov [13] 96.08

Luukka [25] 98.19

Evsukoff et. al. [12] 96.63

Kim and Ryu [20] 96.66

Tsipouras et. al. [42] 95.71

Reyes and Sipper [35] 98.25

This paper 98.42

TABLE 5COMPARATIVE RESULTS OF PID DATASET WITH OTHER

TECHNIQUES

Technique by Accuracy (%)

Tsipouras et. al. [42] 77.30

Kim and Ryu [20] 77.00Evsukoff et. al. [12] 76.82

Hu [15] 75.80

Kukkurainen and Luukka [21] 74.40

Cornelis et. al [9] 73.45

This paper 78.17

Membership function

v1 v2 v3 v4 v5 v6 v7 v8 diabetes

P 10 140 61 35 443 3 7 86 1

d 15 137 59 0 171 13 5 6 3

Rule 1: IF (Diastolic blood pressure IS high) AND (Body mass index IS

high) THEN (diabetes IS negative)

Rule 2: IF (Number of times pregnant IS low) AND (Plasma glucose

concentration a 2 h in an oral glucose tolerance test IS low)

AND (Diastolic blood pressure IS low) AND (Triceps skin

fold thickness IS high) AND (Body mass index IS high)

THEN (diabetes IS positive) Rule 3: IF ( pedigree function IS low) THEN (diabetes IS negative)

Fig. 7. The Best model on PID dataset.

TABLE 6

A COMPARISON OF ONE FITNESS LEVEL WITH TWO FITNESS

LEVELS

Fitnesslevel

Dataset (Average Accuracy)

WBCD dataset(%) PID dataset (%)

1 level 92.17 53.82

2 level 98.42 78.17

Membership function

v1 v2 v3 v4 v5 v6 v7 v8 v9 cancer

P 3 2 1 5 2 3 7 1 7 5

d 8 5 1 1 2 5 6 3 4 2

Rule 1: IF (clump thickness IS high) AND (uniformity of cell shape IS

high) AND (single epithelial cell size IS high) AND (bland

chromatin IS low) then (cancer IS malignant)

Rule 2: IF (uniformity of cell size IS low) THEN (cancer IS benign)

Fig. 6. The Best model on WBCD dataset.






graph that demonstrates the comparison. In Fig. 10, itshows the comparison on the WBCD dataset. The learn-ing process of FCoGA with three species resulted in thefirst 10 generation before becoming stable. On the other

hand, FCoGA with single species occurred in the genera-tion 15 to 50. For the PID dataset, the learning process onthree species and on single species occurred in the gener-ation 5. Even though the learning process occurred in thesame generation, but the fitness value of single species isnot as high as compared to the three species. This isshown in Fig. 11. In conclusion, FCoGA with three specieshas the highest capability of learning the problems inwhich it can learn the problems at the early generation.Therefore, as a plus advantage, FCoGA only needs asmall number of maximum generations.

5 CONCLUSION

In this paper, an improved method of generating fuzzymodel called as FCoGA, has been proposed. FCoGA isdesigned to improve current accuracy rates and increasethe ease of interpretation regarding generated fuzzymodels compared to other previously reported methods.FCoGA is built on top of GA optimisation method. Fol-lowing this, GA is extended by using CCA method with

the intention of reducing the complexity of the solutions.CCA method breaks the chromosomes in GA into threespecies that represent the parameters of the fuzzy model:the fuzzy rule set, the membership functions and theoverlap lengths in the membership functions. In the evo-lution process, each species is evolved separately beforebeing combined with others to complete fuzzy model. Inaddition, FCoGA has two stages of evaluation that arebased on fitness: species fitness and cooperative chromo-some fitness. The fitness is applied to all species with thepurpose of improving the accuracy of the model and toensure that FCoGA obtains the ‘best’ fuzzy model. For thepurpose of performance measurement, FCoGA is tested

on two famous benchmark datasets, the WBCD and thePID, and shows better results than those reported by pre-vious studies. Future research will strive to improve theability of FCoGA to classify non-binary classifications.Consequently, one or more new fuzzy parameters mustbe identified to reduce the complexity of FCoGA whilemaintaining its interpretability.

ACKNOWLEDGMENT

This study has been performed under project Vote 79278and is fully funded by the Malaysian Ministry of Science,Technology and Innovation (MOSTI). Many thanks are

offered to the reviewers whose comments and sugges-tions have improved the paper

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