A new similarity measure between intuitionistic fuzzy sets and the positive definiteness of the similarity matrix

As a generation of fuzzy set theory, intuitionistic fuzzy (IF) set theory has received considerable attention for its capability on dealing with uncertainty. Similarity measures of IF sets are used to indicate the degree of commonality between IF sets. Although several similarity measures for IF sets have been proposed in previous studies, some of those cannot satisfy the axiomatic definitions of similarity, or provide counter-intuitive cases. In this paper, a new similarity measure between IF sets is proposed. The definition of similarity matrix is also presented to depict the relations among more than two IF sets. It is proved 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 can be applied to define a positive definite similarity matrix.