The similarity measure between Interval Type-2 Fuzzy Sets based on triangles

Interval type-2 fuzzy sets (IT2 FSs) has been used in wide range of applications, such as decision making, pattern recognitions. However, there is little investigation on the clustering techniques of IT2 FSs, since it is very important for measuring the degree of similarity between interval type-2 fuzzy sets in clustering research. In this paper, we give a novel method to represent interval type-2 fuzzy sets by a series of linear functions. This method is named as triangular representation because the curves of the functions and the coordinates shape into triangles. A new kind of similarity between interval type-2 fuzzy sets based on triangle is given and the validity of this method is proven. Furthermore, several numerical examples are given to show that the proposed similarity measure is reasonable and better than any existing methods.