On equivalence classes of fuzzy connectives-the case of fuzzy integrals

Michel Grabisch B

83 citations0/0 files storedIEEE Transactions on Fuzzy Systems

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Multi-Criteria Decision Making Advanced Algebra and Logic Fuzzy and Soft Set Theory

Abstract

An equivalence relation between connectives (or operators) in the framework of multiple criteria decision-making is introduced. Two operators are said to be equivalent if they lead to the same ranking of alternatives. Some general results to find equivalence classes of operators are given through the concept of level surfaces. In a second part, these results are applied to the case of discrete fuzzy integrals, which are considered here as n-place operators. First, some general results on the situation of fuzzy integrals among fuzzy operators are given and then the equivalence classes of fuzzy integrals.>

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References

1988On ordered weighted averaging aggregation operators in multicriteria decisionmaking 1994Fuzzy Preference Modelling and Multicriteria Decision Support 1985A review of fuzzy set aggregation connectives 1979Mathematical Methods of Game and Economic Theory 1989An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy measure 1995Characterization of the ordered weighted averaging operators 1993Some quantities represented by the Choquet integral

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