Contrast Similarity Measures of Fuzzy Sets

Authors

Ildar Batyrshin, Instituto Politecnico Nacional
Olga Kosheleva, The University of Texas at El PasoFollow
Vladik Kreinovich, The University of Texas at El PasoFollow
Nailya Kubysheva, Kazan Federal University
Raouf Akhtiamov, Kazan Federal University

Publication Date

4-2019

Comments

Technical Report: UTEP-CS-19-30a

To appear in Proceedings of the World Congress of the International Fuzzy Systems Association and the Annual Conference of the North American Fuzzy Information Processing Society IFSA/NAFIPS'2019, Lafayette, Louisiana, June 18-22, 2019

Abstract

The paper proposes a new class of fuzzy set similarity measures taking into account the proximity of membership values to the border values 0 and 1. These similarity measures take values in [0,1] and generalize the crisp weak equality relation of fuzzy sets considered in the theory of fuzzy sets. The method of construction of a contrast similarity measure using a bipolar function symmetric with respect to 0.5 is presented. The similarity measure defined by the contrast intensification operation considered by Lotfi Zadeh is discussed.