New bounded variation based similarity measures between Atanassov intuitionistic fuzzy sets for clustering and pattern recognition

Abstract

The distance and similarity measures are two interrelated depictions of the patterns which signify the categorization between the Atanassov intuitionistic fuzzy sets (AIFSs) by evaluating the degree of belongingness. In this work, we propose a new similarity measure, termed as hybrid similarity measure, by the combination of intuitionistic fuzzy bounded variation (IFBV) and intuitionistic fuzzy metric based measures. The concept of IFBV which is a technique to approximate arc length of an intuitionistic fuzzy-valued function (IFVF) is also introduced here. The IFVF over an AIFS is geometrically evolved through the generalization of the p-summable IFBV, that is, connecting all the elements of AIFS lie on the structure of IFBV corresponding to power p. The proposed measure overcomes the shortcomings of intuitionistic fuzzy metric based similarity measures by incorporating more flexibility into it. The hybrid similarity measure has been successfully implemented and applied on the several real-world applications in the field of pattern recognition as well as clustering. Further, a detailed comparison of results has been shown against the other existing similarity measures to demonstrate the superiority and validity of the proposed hybrid similarity measure.