Physical Sciences and Mathematics Commons^™

Contrast Similarity Measures Of Fuzzy Sets, Ildar Batyrshin, Olga Kosheleva, Vladik Kreinovich, Nailya Kubysheva, Raouf Akhtiamov

Departmental Technical Reports (CS)

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.