Similarity measures for general type-2 fuzzy sets based on the α-plane representation

Similarity measures are very important concepts in fuzzy sets (FSs) theory. There are many different definitions of similarity measures for both type-1 (T1) FSs and interval type-2 (IT2) FSs. In this paper, one similarity measure for IT2 FSs, which is extended from the Jaccard similarity measure for T1 FSs, is reviewed; then, based on the α-plane representation for a general type-2 (GT2) FS, this similarity measure is generalized to such T2 FSs. Some examples that demonstrate how to compute the similarity measures for different T2 FSs are given.