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

Michel Grabisch and Pedro Miranda ()

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Abstract: We investigate in this paper about the set of $k$-additive capacities dominatinga given capacity, which we call the $k$-additive core. We study its structurethrough achievable families, which play the role of maximal chains in theclassical 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 coreis still an open question.

Keywords: core; capacity; k-additive capacity; game (search for similar items in EconPapers)
Date: 2006-09
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Published in 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)

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Working Paper: A study of the k-additive core of capacities through achievable families (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-00179839

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