Efficient algorithms for computing a class of subsethood and similarity measures for interval type-2 fuzzy sets

Subsethood and similarity measures are important concepts in fuzzy set (FS) theory. There are many different definitions of them, for both type-1 (T1) FSs and interval type-2 (IT2) FSs. In this paper, Rickard et al.'s definition of IT2 FS subsethood measure, extended from Kosko's T1 FS subsethood measure using the Representation Theorem, and Nguyen and Kreinovich's IT2 FS similarity measure, extended from the Jaccard similarity measure for T1 FSs, are introduced. Efficient algorithms for computing them are also proposed. Simulations demonstrate that our proposed algorithms outperform existing algorithms in the literature.