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

A fuzzy c-means (FCM) variant is proposed for the generation of fuzzy term sets with 2 overlap. The proposed variant di5ers from the original mainly in two areas. The 6rst modi6cation ensures that two end terms take the maximum and minimum domain values as their centers. The second modi6cation prevents the generation of non-convex fuzzy terms that often occurs with the original algorithm. The optimal number of terms and the optimal shape of the 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 a5ect the shape of the membership function. The e5ect of data size used for the generation of fuzzy terms is also discussed. A generalized -shaped function with a tunable parameter along with its complement is developed to 6t all term sets generated by the FCM variant using various m values. c © 2002 Elsevier Science B.V. All rights reserved.