Automatic Identification of Fuzzy Models with Modified Gustafson-Kessel Clustering and Least Squares Optimization Methods

An automated method to generate fuzzy rules and membership functions from a set of sample data is presented. Our method is based on clustering and uses a modified version of Gustafson-Kessel algorithm. The aim is to divide a product space into set of clusters for which the systems exhibits behavior close to linear. For each of the clusters we produce a fuzzy rule and generate a set of membership functions for the rule antecedent with use of an approach based on curve fitting. Weighted linear least-squares regression is used to obtain consequent functions for TSK-models.

[1]  Ferenc Szeifert,et al.  Modified Gath-Geva fuzzy clustering for identification of Takagi-Sugeno fuzzy models , 2002, IEEE Trans. Syst. Man Cybern. Part B.

[2]  Gwilym M. Jenkins,et al.  Time series analysis, forecasting and control , 1972 .

[3]  Liang Wang,et al.  Complex systems modeling via fuzzy logic , 1996, IEEE Trans. Syst. Man Cybern. Part B.

[4]  James M. Keller,et al.  Learning the Fuzzy Connectives of a Multilayer Network Using Particle Swarm Optimization , 2007, 2007 IEEE Symposium on Foundations of Computational Intelligence.

[5]  Kazuo Tanaka,et al.  Successive identification of a fuzzy model and its applications to prediction of a complex system , 1991 .

[6]  Antonio F. Gómez-Skarmeta,et al.  About the use of fuzzy clustering techniques for fuzzy model identification , 1999, Fuzzy Sets Syst..

[7]  Jyh-Shing Roger Jang,et al.  ANFIS: adaptive-network-based fuzzy inference system , 1993, IEEE Trans. Syst. Man Cybern..

[8]  Donald Gustafson,et al.  Fuzzy clustering with a fuzzy covariance matrix , 1978, 1978 IEEE Conference on Decision and Control including the 17th Symposium on Adaptive Processes.

[9]  Michio Sugeno,et al.  A fuzzy-logic-based approach to qualitative modeling , 1993, IEEE Trans. Fuzzy Syst..

[10]  Frank Klawonn,et al.  Constructing a fuzzy controller from data , 1997, Fuzzy Sets Syst..

[11]  Weina Wang,et al.  On fuzzy cluster validity indices , 2007, Fuzzy Sets Syst..

[12]  Thomas F. Coleman,et al.  An Interior Trust Region Approach for Nonlinear Minimization Subject to Bounds , 1993, SIAM J. Optim..