A similarity measure between interval type-2 fuzzy sets

The fuzzy similarity measure shows the similar degree of two fuzzy sets (FSs) and can be used in various areas. There are numerous studies as to it on type-1 fuzzy sets (T1 FSs), but little attention has been received on type-2 fuzzy sets (T2 FSs). In this paper, a new similarity measure between interval type-2 fuzzy sets (IT2 FSs) is proposed. Firstly, we select an axiomatic definition for the new similarity measure. Then, according to the selected definition, we propose a computation formula. Finally, we give examples to explain its calculation and combine it with Yang and Shih's clustering method for an application of clustering analysis of Gaussian IT2 FSs. The results show that the proposed similarity measure is reasonable and acceptable for IT2 FSs.