Distance measures on intuitionistic fuzzy sets based on cross-information dissimilarity and their diverse applications

Abstract

In this paper, two new distance measures are introduced, which might be used in various application problems in decision-making, pattern recognition, and clustering. Intuitionistic fuzzy sets are sources of information that contain both the membership and non-membership degrees of the elements in the set. As such, distance measures based on geometric concepts are sometimes misleading. Hence, six parameters are identified to construct the distance measures. These parameters are membership information dissimilarity, non-membership information dissimilarity, hesitancy information dissimilarity, product cross-information dissimilarity, maximum cross-information dissimilarity, and minimum cross-information dissimilarity. Among all the parameters, the product cross-information dissimilarity is being newly introduced in this work. Compensations for the proposed distance measures are established by various counterintuitive problems in decision-making and pattern recognition. Finally, validation of the proposed distance measures is established by diverse problems of applications in decision-making, pattern recognition, and clustering problems.