Self generated fuzzy membership function using ANN clustering technique

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1 Self generated fuzzy membership function using ANN clustering technique Shruti S. Jamsandekar Department of Computer Studies, SIBER, Kolhapur. (MS), India Ravindra R. Mudholkar Department of Electronics Shivaji University, Kolhapur, (MS), India Abstract: In this paper we have proposed a method for self generating the membership functions using semi unsupervised learning method, We have tried to combine trapezoidal and triangular membership function and generate it by neural network clustering technique. Clustering of underlying data to obtain the cluster with cluster centers. These cluster centers are used to formulate membership function centers. The overlapping membership function end vertex are formulated by approximating boundary values of each cluster obtained. An fuzzy Inference system is created based on membership function generated for classification problem Keywords: fuzzy classification, clustering, neural network membership function I. INTRODUCTION Fuzzy classification systems can be used to deal with classification problems. Todevelop a fuzzy classification system, the most important task is to construct membershipfunctions and to find a set of suitable fuzzy rules in the fuzzy classification system. Thereare two approaches to generate fuzzy membership functions andfuzzy rules. Expert knowledge and data driven, these approaches correspond to either manual or automatically through a machine learning process based on training instances respectively.using expert knowledge can be advantages as it has link with domain knowledge but it can be too subjective with different experts generating different membership functions and rules for same application. Alternatively automatic generation of fuzzy membership functions based on data will convert crisp data into linguistic terms. Most previous attempts in automatic generation of fuzzy membership functions have used evolutionary and statistical methods [1, 3,4,7,11].In this paper, we present a new method for constructing membership functions using semi supervised clustering technique, based on cluster centers and approximation of boundary values of each cluster obtain, we tried to present an data driven approach to generate membership function by clustering algorithm for creation of if then fuzzy classification system to deal with student semester examination data. The rest of this paper is organized as follows. In Section II related work in related field is reviewed. In section III, we briefly review of basic concepts of fuzzy setsand the proposed method to construct membership functions based on clustering is explained. In section IV we compare the experimental results of the proposed method with the existing methods. The conclusions are discussed in Section V. II. RELATED WORK [1] proposed a framework for automatic generation of fuzzy membership functions and fuzzy rules from training data,.the approach is based on finding the near optimal fuzzy membership functions through an optimization process using genetic algorithm In [2] authors have proposed an approach to deal with the classification problem using fuzzy logic,to show how fuzzy logic introduces new elements in the identification process. In [3] use the concept of Interval-Valued Fuzzy Set to deal with the problem of degree of uncertainty in the definition of the fuzzy partitions.and to show the improvement in the performance of linguistic Fuzzy Rule-Based Special Issue - IDEAS ISSN: X

2 Classification Systems afterward the application of a cooperative tuning methodology between the tuning of the amplitude of the support and the lateral tuning(based on the 2-tuples fuzzy linguistic model) applied to the linguistic labels modeled with Interval-Valued Fuzzy Sets. Roberto R.F. Mendes et.al in [4] proposes a co-evolutionary system for discovering fuzzy classification rules. The system uses two evolutionary algorithms: a genetic programming(gp) algorithm evolving a population of fuzzy rule sets and a simple evolutionary algorithm evolving a population of membership function definitions. The two populations co-evolve, so that the final result of the co-evolutionary process is a fuzzy rule set and a set of membership function definitions which are well adapted to each other. [5] proposed a new scheme to generate fuzzy membership functions with unsupervised learning using selforganizing feature map. [6] Proposed a fuzzy error backpropogation algorithm based on standard BP algorithm with multilayer neural network to learn fuzzy sets and also learn fuzzy rules by reducing hidden neurons from the network. Shyi-Ming Chen et.al [7] proposed a new method to construct membership function for Iris data classification problem by generating fuzzy rules from training instances based on the correlation coefficient threshold value, the boundary shift value and the center shift value. [8] They proposed an idea of using numerical data for generation and reduction fuzzy rules and adjustment of membership function, generated fuzzy rule base using Mendel & Wang method and compute the degree of similarity between each rule for candidate rule selection, used absolute value of the distance between numerical data to compare with base intersection distance of the membership function.[9] Mehmet kaya et.al proposed a clustering approach to solve the problem of interval partitioning to construct and optimize fuzzy membership based on Genetic algorithm. [10] Jonathan M et.al presented a case study in which the introduction of vagueness or uncertainty into the membership functions of a fuzzy system was investigated in order to model the variation exhibited by experts in a medical decision-making context. Xi Che[11] presented a method by combining the recursive least-squares algorithm and membership to overcome the shortcoming of traditional linear regression used in parameter estimation.bai and Chen [12] presented a new method for evaluating student s learning achievement using Fuzzy Membership Functions and Fuzzy Rules. Ma and Zhou [13] presented a Fuzzy Set approach to the assessment of student centered learning.khairul A. Rasmani and QiangShen [14] have presented a fuzzy rule-based approach for aggregation of student academic performance. The membership values produced by this method were more meaningful compared to the values produced by statistical standardized-score.oyelade, O. J et.al [15] proposed a method for analyzing students results based on cluster analysis and uses standard statistical algorithms to arrange their scores data according to the level of their performance implemented k-means clustering algorithm for analyzing students result data. III. NEW METHOD TO GENERATE MEMBERSHIP FUNCTIONS BASED ON CLUSTERING A. Overview of Fuzzy logic A fuzzy set A in a universe of discourse X is defined as the following set pairs Where, µ A (x) :X [0,1] is a mapping called the membership function of fuzzy set A and µ A (x)is called the degree of belongingness or membership value or degree of membership of x X in the fuzzy set A. wewrite (1) in the following form: For brevity, however, we often equate fuzzy sets with their membership functions i.e. instead of a fuzzy set A characterized by µ A (x) we will often say fuzzy sets µ A [4, 8]. Example: Suppose X = {6, 2, 0, 4}. A fuzzy set of X may be given by A = {0.2/6, 1/2, 0.8/0, 0.1/4}. Construction of membership function is based on the system design data and choice of the suitable shape. There are many shapes of membership functions. However, the application context dictates the choice of the suitable shape. For the problem domain addressed in this study, system components have maximum and minimum value that cannot be exceeded. Therefore, any candidate membership function shape should have two extreme bounds with zero and hundred as range values. Triangular and trapezoidal shapes are the simplest MF shapes that meet this requirement. (2) (1) Special Issue - IDEAS ISSN: X

3 The membership function of the triangularfuzzy set A can be represented by a triple (b; c; a), where \c" is called the center of thetriangular fuzzy set A; \b" is called the left vertex of the triangular fuzzy set A; \a" iscalled the right vertex of the triangular fuzzy set A. The membership function of the trapezoidal fuzzy set can be represented by a function of a vector, x, and depends on four scalar parameters a, b, c, and d, as given by Figure 2. Trapezoidal Membership Function B. Proposed work- (4) Special Issue - IDEAS ISSN: X

4 The type of membership functions we use in this paper is the triangularand trapezoidal membership function as shown in Figure.1 and Figure.2 respectively. The extreme ends membership functions are trapezoidal and inner membership function are triangular. The construction of triangular membership functions are based on the cluster the data. Referring to Figure.1c ie the center of triangular fuzzy set is calculated based on cluster centers C. The steps carried out to construct membership functions for input variables are as follows- 1. Clustering is done on student examination data and cluster centers are found. 2. Clustering algorithm used is neural network clustering technique based on SOM,for each subject marks to form 3 cluster based on weight vector obtained. The three cluster center are formed based on mean average method and forms the centers of 3 inner triangular fuzzy membership function 3. The left and right vertex of each of the triangular fuzzy membership function referring to Figure 1. b and a are calculated as follows. 3.1 Find maximum and minimum data value of each cluster formed from weight vectors 3.2 Approximated the maximum by 10% increase to form right vertex of the membership function and minimum by 10% decrease to form the left vertex of the membership function, this is done for overlapping the membership functions. 4. The two extreme end trapezoidal membership functions are constructed as follows 4.1 First extreme membership function according to figure 2 a, b with zero value and c and d is calculated c= Min( Minimum of each clusters) (0.1 * Min( Minimum of each clusters) ) d = Min( Minimum of each clusters) + (0.15 * Min( Minimum of each clusters) ) 4.2 second extreme membership function according to figure 2 c, d with 100 value and a and b is calculated a = max(maximum of each cluster) (0.1 * Max( maximum of each clusters) ) b= max(maximum of each cluster) + (0.05 * Max( maximum of each clusters) ) D. The steps carried out to construct membership functions for output variables are as follows- 1. The output variable also comprises of 5 membership functions same as input variable the range for triangular membership function is calculated as follows 2. Average of centers of first cluster, second cluster and third cluster for all input variables to form the centers of three triangular membership function respectively 3. To find left and right vertex of 3 triangular membership for output variable 3.1 Left vertex of each of the 3 triangular membership function is Average of minimum Offirst cluster, second cluster and third cluster for input variable(calculated in step 3.1 of input variable) respectively 3.2 To find Right vertex of each of the 3 triangular membership function is Average of maximum of first cluster, second cluster and third cluster for input variable (calculated in step 3.1 of input variable) respectively. 4. The two extreme end trapezoidal membership functions are selected based as follows 4.1 First extreme membership function according to figure 2 a, b with zero value and c and d is c= 20 and d= 35 (as per passing criteria since the domain data is student examination marks ) 4.2Second extreme membership function according to figure 2 c, d with 100 value and a and b is calculated a = max(maximum of each cluster) (0.1 * Max( maximum of each clusters) ) b= max(maximum of each cluster) + (0.05 * Max( maximum of each clusters) ) Special Issue - IDEAS ISSN: X

5 IV. ILLUSTRATION OF PROPOSED METHOD AND EXPERIMENTAL RESULTS The experiment is carried using matlab fuzzy tool and neural network clustering tool. Comparision of the experimental results of the proposed method with the existing methods A. To illustrate the method proposed - 1. Accept the student examination data. Student data set for two subject marks in semester exam is shown in Appendix A 2. Clustering the student data using neural network clustering algorithm 2.1 The cluster center for subject 1 data are center of three triangular membership functions of input variable The cluster center for subject 2data are center of three triangular membership functions of input variable The left and right vertex of the 3 triangular membership function 3.1 The maximum and minimum for subject 1 Max Min The maximum and minimum for subject 2 Max Min Approximate values calculated for overlapping of membership Left and right vertex of the 3 triangular membership function for input Special Issue - IDEAS ISSN: X

6 Left and right vertex of the 3 triangular membership function for input 2 The following is the membership function generated of input1, input2 variablesfor subject1 and subject 2 respectively using steps of section III very l ow low medium high very h igh 1 very l ow low medium high very h igh Degree of membership Degree of membership sub1 m arks sub2 m arks (a) (b) The following is the membership function generated for output variables of fuzzy inference system for classification using steps of section III Special Issue - IDEAS ISSN: X

7 1 poor below a vg avg above a vg good 0.8 Degree of membership class (c) 3.3 The rule base list for Inference created Input 1 variable value Input 2 variabe vale Output variable value Weight Connection (AND/OR ) \ Table 1: Rule List B. Experimental Results Snapshot of results obtained by proposed Fuzzy Classification based on Membership function generated by ANN Clustering (FCMANNC) and Fuzzy classification based on membership function constructed using expert domain knowledge. The detail result in shown in Appendix B Special Issue - IDEAS ISSN: X

8 (a) V CONCLUSION The paper describes a new method of fuzzy classification with membership function generated using semi supervised clustering approach. The method was experimented on student examination data,when the results in Appendix B are observed the subject values in lower range of and higher range of in Appendix A, a variations in outcome is seen between the class values that are created based on the fuzzy membership function based on domain expert knowledge and proposed self generated membership functions method for classification. For all middle range values the class values obtained are similar for both the compared methods. REFERENCES [1] MasoudMakrehchia, Mohamed S. Kamelb, An information theoretic approach to generating fuzzy hypercubes for if-then classifiers, Journal of Intelligent & Fuzzy Systems vol. no 22pp: (2011) [2] Dinesh P.Pitambare, PravinM.Kamde, Fuzzy Classification System for Glass Data Classification, International Journal of Engineering Research (ISSN : )Volume No.2, Issue No.2, pp : April 2013 [3] J. Sanz, et.al, A Genetic Algorithm for Tuning Fuzzy Rule-Based Classification Systems with Interval-Valued Fuzzy Sets WCCI 2010 IEEE World Congress on Computational Intelligence July, 18-23, CCIB, Barcelona, Spain [4] Roberto R.F. Mendes et.al Discovering Fuzzy Classification Rules with Genetic Programming and Co-evolution, LNAI 2168, pp , Springer-Verlag Berlin Heidelberg 2001 [5] Chih-Chung Yang, N.K. Bose, Generating fuzzy membership function with self-organizing feature map, Elsevier, Pattern Recognition Letters (2006) [6] DetlefNauck, Rudolf Kruse, Fuzzy NeuralNetwork learning Fuzzy Control Rules and Membership functions by Fuzzy Error Backpropagation,IEEEInt.Conf on Neural Network ICNN 93,san Francisco Apr 1993 [7] Shyi-Ming Chen Fu-Ming Tsai, A New Method to Construct Membership Functions and Generate Fuzzy Rules from Training Instances,Journal of Information and Management Sciences Volume 16, Number 2, pp , 2005 [8] RaoufKetata, HatemBellaaj, Mohamed Chtourou, Mohamed Ben Amer, Adjustment Of Membership Functions, Generation And Reduction Of Fuzzy Rule Base From Numerical Data, Malaysian Journal of Computer Science, Vol. 20(2), pp [9] Mehmet Kaya, RedaAlhajj Utilizing Genetic Algorithms to Optimize Membership Functions for Fuzzy Weighted Association Rules Mining,Applied Intelligence, Springer Science and Business Media vol. 24, pp:7 15, [10] Jonathan M. Garibaldi and TurhanOzen, Uncertain Fuzzy Reasoning: A Case Study in Modelling Expert Decision Making,IEEE Transactions On Fuzzy Systems, Vol. 15, No. 1, February 2007 [11] Xi Che, Recursive Least-Squares Method With Membership Functions, Proceedings of the Third International Conference on Machine Learning and Cybernetics, Shanghai, August 2004 [12] S. M. Bai and S. M. Chen, "Evaluating students' learning achievement using fuzzy membership functions and fuzzy rules," IEEE Expert Systems with Applications, vol. 34, no. 1, pp , [13] J. Ma and D. Zhou, "Fuzzy set approach to the assessment of student-centered learning," IEEE Transactions on Education, vol. 43, no. 2, pp , [14] Khairul A. Rasmani and QiangShen, Data-Driven Fuzzy Rule Generation and its Application for Student Academic Performance Evaluation, Journal on Applied Intelligence, vol. No.25,pp , 2006 Special Issue - IDEAS ISSN: X

9 [15] Oyelade, O. J, Oladipupo, O. O, Obagbuwa, I. C, Application of k-means Clustering algorithm forprediction of Students Academic Performance,(IJCSIS) International Journal of Computer Science and Information Security,Vol. 7, No. 1,pp: , 2010 APPENDIX A Seat no Subject 1 Subject Special Issue - IDEAS ISSN: X

10 Seat no APPENDIX B Fuzzy class using FCMC Fuzzy class using expert domain Special Issue - IDEAS ISSN: X

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