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