Fuzzy clustering analysis for optimizing fuzzy membership functions

Fuzzy model identification is an application of fuzzy inference system for identifying unknown functions, for a given set of sampled data. The most important thing for fuzzy identification task is to decide the parameters of membership functions (MFs) used in fuzzy systems. A lot of efforts (Chung and Lee, 1994; Jang, 1993; Sun and Jang, 1993) have been given to initialize the parameters of fuzzy membership functions. However, the problems of parameter identification were not solved formally. Assessments of these algorithms are discussed in the paper. Based on the fuzzy c-means (FCM) Bezdek (1987) clustering algorithm, we propose a heuristic method to calibrate the fuzzy exponent iteratively. A hybrid learning algorithm for refining the system parameters is then presented. Examples are demonstrated to show the effectiveness of the proposed method, comparing with the equalized universe method (EUM) and subtractive clustering method (SCM) Chiu (1994). The simulation results indicate the general applicability of our methods to a wide range of applications. (C) 1999 Elsevier Science B.V. All rights reserved.