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Article Dans Une Revue European Journal of Operational Research Année : 2007

Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison

Louis Aimé Fono
  • Fonction : Auteur
Henri Gwet
  • Fonction : Auteur

Résumé

In this paper, we determine by means of fuzzy implication operators, two classes of difference operations for fuzzy sets and two classes of symmetric difference operations for fuzzy sets which preserve properties of the classical difference operation for crisp sets and the classical symmetric difference operation for crisp sets respectively. The obtained operations allow us to construct as in [B. De Baets, H. De Meyer, Transitivity-preserving fuzzification schemes for cardinality-based similarity measures, European Journal of Operational Research 160 (2005) 726–740], cardinality-based similarity measures which are reflexive, symmetric and transitive fuzzy relations and, to propose two classes of distances (metrics) which are fuzzy versions of the well-known distance of cardinality of the symmetric difference of crisp sets.

Dates et versions

hal-01172254 , version 1 (07-07-2015)

Identifiants

Citer

Louis Aimé Fono, Henri Gwet, Bernadette Bouchon-Meunier. Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison. European Journal of Operational Research, 2007, 183 (1), pp.314-326. ⟨10.1016/j.ejor.2006.10.001⟩. ⟨hal-01172254⟩
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