Inclusion based robust clustering of fuzzy sets

In this paper, a new robust clustering methodology based on a genetic algorithm is proposed. The problem of interest is clustering an input set of fuzzy membership functions which in the past have been clustered using an inclusion index. Two distinct measures based on the inclusion index are also proposed for use as fitness functions for the genetic algorithm. The inclusion index-based fitness criteria are proposed as a replacement for criteria that use some kind of distance as a measure of similarity. The proposed methodology is also robust against outliers in the input set of membership functions, assuming that parameters of one or more sets may have been defined erroneously. Another distinct advantage of the proposed methodology is the fact that the number of clusters need not be defined a priori - the genetic algorithm rewards those partitions that cluster for the most optimal number of clusters based solely on the inclusion index. The proposed genetic algorithm-based inclusive clustering method is tested on two well-known data sets from literature and results comparing performance of the proposed algorithm to those reported in literature are presented.