Monotonic similarity measures between intuitionistic fuzzy sets and their relationship with entropy and inclusion measure

Similarity measure is an important tool for determining the degree of similarity between two objects. Since the introduction of intuitionistic fuzzy sets, similarity measures between intuitionistic fuzzy sets have gained attention for their application in various fields. In this paper, the monotonicity of similarity measures between intuitionistic fuzzy sets are investigated. Firstly, by means of analyzing the geometrical relation between intuitionistic fuzzy sets, three types of monotonicity properties are defined. And then, the properties and the relationship with entropy and inclusion measure of these monotonic similarity measures are discussed. Finally, some existing monotonic similarity measures in literature are summarized and some new monotonic similarity measures and their applications are proposed and presented.