On Lower and Upper Approximation of Fuzzy Measures by k-Order Additive Measures

Michel Grabisch 1
1 SYSDEF - Systèmes d'aide à la décision et à la formation
LIP6 - Laboratoire d'Informatique de Paris 6
Abstract : We extend the result of Chateauneuf and Jaffray on upper and lower approximations of a fuzzy measure (capacity) by a probability measure to the case of k-additive measures, i.e. capacities for which the Möbius transform vanishes for subsets of more than k elements. A necessary condition is given, and the relation with the interaction index is given for 2-additive measures.
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Michel Grabisch. On Lower and Upper Approximation of Fuzzy Measures by k-Order Additive Measures. Information, Uncertainty, Fusion, 516, Kluwer Academic Publishers, pp.105-118, 2000, The Springer International Series in Engineering and Computer Science, ⟨10.1007/978-1-4615-5209-3_8⟩. ⟨hal-01573477⟩

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