A Generalization of Similarity Measure in Collection of Intuitionistic Fuzzy Sets

A collection of intuitionistic fuzzy sets is a new approach to intuitionistic fuzzy set theory. In collections of intuitionistic fuzzy sets, a similarity measure can determine the degree of similarity based on the information carried by the collections. However, an existing similarity measure is limited to evaluating similarity between two collections defined over the same universal set. To overcome this limitation, thus, in this paper, we propose a generalized similarity measure that can be applied to collections defined over different universal sets. To construct the generalization, we first introduce the concept of inferior and equivalent relations in the collection of intuitionistic fuzzy sets. Then, we present a new formula for the similarity measure. Finally, the proposed measure is illustrated through a pattern recognition problem to demonstrate its effectiveness and practical value.