A novel similarity measure on intuitionistic fuzzy sets with its applications

The intuitionistic fuzzy set, as a generation of Zadeh' fuzzy set, can express and process uncertainty much better, by introducing hesitation degree. Similarity measures between intuitionistic fuzzy sets (IFSs) are used to indicate the similarity degree between the information carried by IFSs. Although several similarity measures for intuitionistic fuzzy sets have been proposed in previous studies, some of those cannot satisfy the axioms of similarity, or provide counter-intuitive cases. In this paper, we first review several widely used similarity measures and then propose new similarity measures. As the consistency of two IFSs, the proposed similarity measure is defined by the direct operation on the membership function, non-membership function, hesitation function and the upper bound of membership function of two IFS, rather than based on the distance measure or the relationship of membership and non-membership functions. It proves that the proposed similarity measures satisfy the properties of the axiomatic definition for similarity measures. Comparison between the previous similarity measures and the proposed similarity measure indicates that the proposed similarity measure does not provide any counter-intuitive cases. Moreover, it is demonstrated that the proposed similarity measure is capable of discriminating the difference between patterns.