A similarity measure between general type-2 fuzzy sets and its application in clustering

The similarity measure between fuzzy sets is an important concept in fuzzy set theory, but little work as to it has been done on type-2 fuzzy sets. For that, a new similarity measure between general type-2 fuzzy sets is proposed in this paper. Firstly, we select an axiomatic definition for the similarity measure between general type-2 fuzzy sets. Then, based on the selected definition, we propose a computation formula by considering the FOU and the secondary membership function. Finally, we give examples to illuminate its calculation and combine it with Yang and Shih's method for an application to clustering of type-2 fuzzy data. The clustering results consist of a reasonably hierarchical tree in different α-levels and show that the new similarity measure is reasonable for general type-2 fuzzy sets.