论文信息 - A graphical interpretation of the Choquet integral

A graphical interpretation of the Choquet integral

The Choquet integral (1953) is a fuzzy measure used as a powerful aggregation operator over a finite set of elements. We present a graphical interpretation of the Choquet integral, viewed as an aggregation operator in the case of two elements. The interpretation relies on the interaction representation introduced by the author.

Michel Grabisch

[1] M. Sugeno,et al. Some quantities represented by the Choquet integral , 1993 .

[2] L. Shapley. A Value for n-person Games , 1988 .

[3] Michel Grabisch,et al. Application of the Choquet integral in multicriteria decision making , 2000 .

[4] M. Sugeno,et al. An interpretation of fuzzy measures and the Choquet integral as an integral with respect to a fuzzy , 1989 .

[5] Michel Grabisch,et al. Interaction Transform of Set Functions over a Finite Set , 1999, Inf. Sci..

[6] Ronald R. Yager,et al. On ordered weighted averaging aggregation operators in multicriteria decisionmaking , 1988, IEEE Trans. Syst. Man Cybern..

[7] G. Choquet. Theory of capacities , 1954 .

[8] Michel Grabisch,et al. Alternative Representations of Discrete Fuzzy Measures for Decision Making , 1997, Int. J. Uncertain. Fuzziness Knowl. Based Syst..

[9] Michel Grabisch,et al. K-order Additive Discrete Fuzzy Measures and Their Representation , 1997, Fuzzy Sets Syst..

[10] Hung T. Nguyen,et al. Fundamentals of Uncertainty Calculi with Applications to Fuzzy Inference , 1994 .

[11] S. Weber. ⊥-Decomposable measures and integrals for Archimedean t-conorms ⊥ , 1984 .

[12] Michel Grabisch,et al. An axiomatic approach to the concept of interaction among players in cooperative games , 1999, Int. J. Game Theory.