# 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 :
Document type :
Conference papers
Domain :

https://halshs.archives-ouvertes.fr/halshs-00179839
Contributor : Michel Grabisch <>
Submitted on : Tuesday, October 16, 2007 - 5:51:39 PM
Last modification on : Tuesday, March 27, 2018 - 11:48:05 AM

### Identifiers

• 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). ⟨halshs-00179839⟩

Record views