Similarity measure on collection of intuitionistic fuzzy sets

We are aware that intuitionistic fuzzy sets are one of generalization of fuzzy sets. To compare the similarity of information carried by intuitionistic fuzzy sets, similarity measures are constructed. Researchers have explored similarity measure as part of developing intuitionistic fuzzy sets. The similarity measures on intuitionistic fuzzy sets cannot fully answer the problems of measuring similarity that incorporates more complicated characterizations in collection sets. Therefore, we provide a novelty similarity measure. We provide a similarity measure for intuitionistic fuzzy set collections. In this article, first, we propose similarity measure's definition in the collection of intuitionistic fuzzy sets, then new formula of similarity measure with membership value and non-membership value. Moreover, we give proof of a new formula of similarity measure, so it is well defined, and examples to illustrate the proposed similarity measure are given too.