A BIPARAMETRIC FAMILY OF CARDINALITY-BASED FUZZY SIMILARITY MEASURES

Klaas Bosteels () and Etienne E. Kerre ()
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Klaas Bosteels: Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium
Etienne E. Kerre: Department of Applied Mathematics and Computer Science, Ghent University, Krijgslaan 281 (S9), B-9000 Gent, Belgium

New Mathematics and Natural Computation (NMNC), 2007, vol. 03, issue 03, 307-319

Abstract: We present a systematic way of constructing and analyzing fuzzy similarity measures based on cardinality. This is achieved by introducing a general form for such measures, that depends on two parameters. We demonstrate that this general form includes several existing families of fuzzy similarity measures. Moreover, we show that certain properties can be ensured by imposing simple constraints on the parameters. In particular, we present constraints that ensure several forms of restrictability, which allow to reduce the calculation time in practical implementations. To conclude, we illustrate the presented technique by using it to analyze some well-known fuzzy similarity measures.

Keywords: Fuzzy similarity measures; fuzzy cardinality (search for similar items in EconPapers)
Date: 2007
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DOI: 10.1142/S1793005707000793

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