Transitivity-preserving fuzzification schemes for cardinality-based similarity measures. (English) Zbl 1061.90080

De Baets, B.; De Meyer, H.

Eur. J. Oper. Res. 160, No. 3, 726-740 (2005).

Summary: A family of fuzzification schemes is proposed that can be used to transform cardinality-based similarity measures for ordinary sets into similarity measures for fuzzy sets in a finite universe. The family is based on rules for fuzzy set cardinality and for the standard operations on fuzzy sets. In particular, the fuzzy set intersections are pointwisely generated by Frank t-norms. The fuzzification schemes are applied to a variety of previously studied rational cardinality-based similarity measures for ordinary sets and it is demonstrated that transitivity is preserved in the fuzzification process.

MSC:

90B99	Operations research and management science
90C70	Fuzzy and other nonstochastic uncertainty mathematical programming

Keywords:

Similarity measure; Fuzzy similarity measure; Reflexivity; Transitivity; Triangular norm; Frank t-norm

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