# A study of the k-additive core of capacities through achievable families

Abstract : We investigate in this paper about the set of $k$-additive capacities dominating
a given capacity, which we call the $k$-additive core. We study its structure
through achievable families, which play the role of maximal chains in the
classical case ($k=1$), and show that associated capacities are element
(possibly a vertex) of the $k$-additive core when the capacity is
$(k+1)$-monotone. The problem of finding all vertices of the $k$-additive core
is still an open question.
Keywords :
Type de document :
Communication dans un congrès
SCIS-ISIS 2006, 3nd Int. Conf. on Soft Computing and Intelligent Systems and 7th Int. Symp. on Advanced Intelligent Systems, Sep 2006, Yokohama, Japan. no pagination (CD), 2006
Domaine :

https://halshs.archives-ouvertes.fr/halshs-00179839
Contributeur : Michel Grabisch <>
Soumis le : mardi 16 octobre 2007 - 17:51:39
Dernière modification le : mardi 27 mars 2018 - 11:48:05

### Identifiants

• HAL Id : halshs-00179839, version 1

### Citation

Michel Grabisch, Pedro Miranda. A study of the k-additive core of capacities through achievable
families. SCIS-ISIS 2006, 3nd Int. Conf. on Soft Computing and Intelligent Systems and 7th Int. Symp. on Advanced Intelligent Systems, Sep 2006, Yokohama, Japan. no pagination (CD), 2006. 〈halshs-00179839〉

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