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A New Distance for Interval Type-2 fuzzy Sets with an Application to Clustering

Type-2 fuzzy sets are generalizations of ordinary fuzzy sets, in which membership grades are characterized by fuzzy membership functions. Here, a problem of finding distance between two interval type-2 fuzzy sets (IT2-FSs) was considered. Based on a new definition of centroid for an IT2-FS, a formulation for calculation of the distance between two IT2-FSs was introduced, and an algorithm was explained to obtain it. The proposed distance formula was incorporated in Yang and Shih's clustering algorithm to reach a clustering method for interval type-2 fuzzy data sets. The applicability of the proposed distance formula was evaluated using two artificial and real data sets, and reasonable results were obtained.