A kind of monotonic similarity measure of interval-valued fuzzy sets

A similarity measure is a measure that indicates the degree of similarity between two objects. This paper investigates the monotonicity properties of similarity measures of interval-valued fuzzy sets. Firstly, a new kind of similarity measure, named monotonic similarity measure is proposed and investigated through analyzing the geometrical relation between interval-valued fuzzy sets. Furthermore, its properties and relationship with entropy and inclusion measure are studied and discussed. And then, some mew monotonic similarity measures are constructed by means of the proposed relationship. Finally, the applications of the proposed monotonic similarity measures are presented. This research not only introduces a novel kind of similarity measure, but also provides some methods to construct similarity measures, entropies and inclusion measures.