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p-symmetric fuzzy measures

Author

Listed:
  • Pedro Miranda

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

  • Michel Grabisch

    () (SYSDEF - Systèmes d'aide à la décision et à la formation - LIP6 - Laboratoire d'Informatique de Paris 6 - UPMC - Université Pierre et Marie Curie - Paris 6 - CNRS - Centre National de la Recherche Scientifique)

  • Pedro Gil

    (Universidad de Oviedo)

Abstract

In this paper we propose a generalization of the concept of symmetric fuzzy measure based in a decomposition of the universal set in what we have called subsets of indifference. Some properties of these measures are studied, as well as their Choquet integral. Finally, a degree of interaction between the subsets of indifference is defined.

Suggested Citation

  • Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
  • Handle: RePEc:hal:journl:hal-00273960
    DOI: 10.1142/s0218488502001867
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00273960
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    File URL: https://hal.archives-ouvertes.fr/hal-00273960/document
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    Citations

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    Cited by:

    1. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01302377, HAL.
    2. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00625708, HAL.
    3. Pedro Miranda & Michel Grabisch & Pedro Gil, 2006. "Dominance of capacities by k-additive belief functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00186905, HAL.
    4. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A representation of preferences by the Choquet integral with respect to a 2-additive capacity," Theory and Decision, Springer, vol. 71(3), pages 297-324, September.
    5. Zhang, Ling & Zhang, Luping & Zhou, Peng & Zhou, Dequn, 2015. "A non-additive multiple criteria analysis method for evaluation of airline service quality," Journal of Air Transport Management, Elsevier, vol. 47(C), pages 154-161.
    6. Miranda, Pedro & Grabisch, Michel & Gil, Pedro, 2006. "Dominance of capacities by k-additive belief functions," European Journal of Operational Research, Elsevier, vol. 175(2), pages 912-930, December.
    7. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    8. Serena Doria, 2015. "Symmetric coherent upper conditional prevision defined by the Choquet integral with respect to Hausdorff outer measure," Annals of Operations Research, Springer, vol. 229(1), pages 377-396, June.
    9. Michel Grabisch & Christophe Labreuche, 2008. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Post-Print halshs-00267932, HAL.
    10. Pedro Miranda & Michel Grabisch, 2012. "An algorithm for finding the vertices of the k-additive monotone core," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-00806905, HAL.
    11. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A characterization of the 2-additive Choquet integral through cardinal information," Post-Print halshs-00625708, HAL.
    12. Michel Grabisch & Christophe Labreuche, 2004. "Fuzzy measures and integrals in MCDA," Post-Print halshs-00268985, HAL.
    13. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00625706, HAL.
    14. 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.
    15. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) hal-01477514, HAL.
    16. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Post-Print halshs-00496558, HAL.
    17. Pedro Miranda & Michel Grabisch, 2012. "An algorithm for finding the vertices of the k-additive monotone core," Post-Print hal-00806905, HAL.
    18. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
    19. Brice Mayag & Michel Grabisch & Christophe Labreuche, 2009. "A characterization of the 2-additive Choquet integral through cardinal information," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445132, HAL.
    20. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.

    More about this item

    Keywords

    Choquet integral; OWA operator; Fuzzy measures;

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