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

Author

Listed:
  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Pedro Miranda

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.

Suggested Citation

  • Michel Grabisch & Pedro Miranda, 2006. "A study of the k-additive core of capacities through achievable families," Post-Print halshs-00179839, HAL.
    • Handle: RePEc:hal:journl:halshs-00179839
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