A triparametric family of cardinality-based fuzzy similarity measures

Authors:
Klaas Bosteels;Etienne E. Kerre
Affiliations:
Fuzziness and Uncertainty Modelling Research Group, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium;Fuzziness and Uncertainty Modelling Research Group, Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium
Venue:
Fuzzy Sets and Systems
Year:
2007

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Abstract

Previously, we introduced a biparametric family of cardinality-based fuzzy similarity measures. In this paper, we generalize this family by adding a third parameter. We also study the generalized family for specific values of the third parameter. More precisely, we show that for particular values of this parameter, certain properties can be ensured by imposing constraints on the two remaining parameters. To conclude, we examine some members of the presented family of fuzzy similarity measures.