A novel knowledge-based similarity measure on intuitionistic fuzzy sets and its applications in pattern recognition

Similarity measure is a useful tool to determine the similarity of two intuitionistic fuzzy sets (IFSs). Theoretically, there are two free variables of membership and non-membership on IFSs, and the most fuzzy set is not solely. Therefore, it is impossible to establish a similarity measure satisfying the classical axiom on it by using only the distance between any given IFSs and the assumed most fuzzy set. The motivation and innovation of this study lies in the exploration and use of the two most fuzzy sets, and the weighted average distance between IFSs and the two most fuzzy sets is used to define the similarity measure. Based on this analysis, a knowledge-based similarity measure on IFSs is proposed and some applications of this proposed measure in pattern recognition are introduced. The advantage of the introduced similarity measure is that it calculates the dissimilarity between the complementary sets well. Furthermore, it proves that the novel similarity measure satisfies axioms of the similarity measure on IFSs, and overcomes the drawbacks of the existing measures. Finally, a series of examples in pattern recognition fields are introduced to demonstrate the effectiveness of the proposed similarity measure.