A fuzzy c-medians variant for the generation of fuzzy term sets

Abstract

A fuzzy c-medians variant is proposed for the generation of fuzzy term sets with one half overlap. The proposed variant is modified from the original algorithm mainly in two areas. The first modification ensures that two end terms take the maximum and minimum domain values as their centers. The second modification prevents the generation of non-convex fuzzy terms that often are obtained by the original algorithm. The optimal number of terms and the optimal shape of membership function associated with each term are determined based on the mean squared error criterion. The exponential weight, m, used in the algorithm is found to greatly affect the shape of membership function. The effect of data size used for the generation of fuzzy terms is also discussed. A generalized s-shaped function with a tunable parameter along with its complement (i.e., a generalized z-shaped function with a tunable parameter) is developed to fit all term sets generated by the fuzzy c-medians variant using various m values. © 2002 John Wiley & Sons, Inc.