A similarity measure for interval type-2 fuzzy sets applied to fuzzy risk analysis

Similarity measures are one of the most significant tools for reasoning in a fuzzy environment. While several similarity measures handle type-1 fuzzy sets, only a few handle type-2 fuzzy sets. This article proposes a similarity measure for trapezoidal interval type-2 fuzzy sets (TrIT2FSs). The proposed similarity measure avoids the flaws of the extant similarity measures for TrIT2FSs. It is a simple method and its calculations are easily performed. The method is a generalization of a similarity measure for generalized type-1 fuzzy sets and an extension of a similarity measure for interval-valued fuzzy sets with simplifications. The method is based on the perimeters, the heights, and the geometric distances of the upper and lower membership functions. A problem in fuzzy risk analysis is solved to illustrate the applicability of the proposed similarity measure to solve these problems.