Fuzzy implication operators for difference operations for fuzzy sets and cardinality-based measures of comparison |
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| Authors: | Louis Aimé Fono Henri Gwet Bernadette Bouchon-Meunier |
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| Institution: | 1. Département de Mathématiques et Informatique, Faculté des Sciences, Université de Douala, B.P. 24157 Douala, Cameroon;2. National Polytechnic Institute, P.O. Box 8390, Yaoundé, Cameroon;3. (UMR-CNRS 7606) APA, Laboratoire d’Informatique de Paris 6 (LIP6), Université de Pierre et Marie Curie (UPMC), 8, rue du capitaine Scott, 75015 Paris, France |
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| Abstract: | 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. |
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| Keywords: | Distance Difference of fuzzy sets Fuzzy similarity measure Symmetric difference of fuzzy sets Transitivity Triangular norm |
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