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p-symmetric bi-capacities


  • Pedro Miranda

    () (UCM - Universidad Complutense de Madrid [Madrid])

  • Michel Grabisch

    () (DECISION - LIP6 - Laboratoire d'Informatique de Paris 6 - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)


Bi-capacities have been recently introduced as a natural generalization of capacities (or fuzzy measures) when the underlying scale is bipolar. They allow to build more flexible models in decision making, although their complexity is of order $3^n$, instead of $2^n$ for fuzzy measures. In order to reduce the complexity, the paper proposes the notion of $p$-symmetric bi-capacities, in the same spirit as for $p$-symmetric fuzzy measures. The main idea is to partition the set of criteria (or states of nature, individuals,\ldots) into subsets whoseelements are all indifferent for the decision maker.

Suggested Citation

  • Pedro Miranda & Michel Grabisch, 2004. "p-symmetric bi-capacities," Post-Print halshs-00188173, HAL.
  • Handle: RePEc:hal:journl:halshs-00188173
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    Cited by:

    1. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
    2. Miranda, P. & Combarro, E.F. & Gil, P., 2006. "Extreme points of some families of non-additive measures," European Journal of Operational Research, Elsevier, vol. 174(3), pages 1865-1884, November.
    3. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
    4. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    5. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477514, HAL.
    6. Michel Grabisch, 2006. "Evaluation subjective," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00179068, HAL.

    More about this item


    p-symmetr; bi-capacity; bipolar scales;


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