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p-symmetric fuzzy measures

Author

Listed:
  • Pedro Miranda

    (UCM - Universidad Complutense de Madrid = Complutense University of 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 = University of 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.science/hal-00273960
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    Citations

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    Cited by:

    1. Pedro Miranda & Michel Grabisch, 2012. "An algorithm for finding the vertices of the k-additive monotone core," Post-Print hal-00806905, HAL.
    2. 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.
    3. 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.
    4. 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.
    5. Michel Grabisch, 2015. "Fuzzy Measures and Integrals: Recent Developments," Post-Print hal-01302377, HAL.
    6. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    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. Jian-Zhang Wu & Yi-Ping Zhou & Li Huang & Jun-Jie Dong, 2019. "Multicriteria Correlation Preference Information (MCCPI)-Based Ordinary Capacity Identification Method," Mathematics, MDPI, vol. 7(3), pages 1-13, March.
    9. 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.
    10. 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.
    11. Chin-Yi Chen & Jih-Jeng Huang, 2019. "Forming a Hierarchical Choquet Integral with a GA-Based Heuristic Least Square Method," Mathematics, MDPI, vol. 7(12), pages 1-16, December.
    12. Li Huang & Jian-Zhang Wu & Rui-Jie Xi, 2020. "Nonadditivity Index Based Quasi-Random Generation of Capacities and Its Application in Comprehensive Decision Aiding," Mathematics, MDPI, vol. 8(2), pages 1-14, February.
    13. 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.
    14. Marichal, Jean-Luc, 2007. "k-intolerant capacities and Choquet integrals," European Journal of Operational Research, Elsevier, vol. 177(3), pages 1453-1468, March.
    15. P. García-Segador & P. Miranda, 2020. "Order cones: a tool for deriving k-dimensional faces of cones of subfamilies of monotone games," Annals of Operations Research, Springer, vol. 295(1), pages 117-137, December.
    16. Yasuo Narukawa & Vicenç Torra & Michio Sugeno, 2016. "Choquet integral with respect to a symmetric fuzzy measure of a function on the real line," Annals of Operations Research, Springer, vol. 244(2), pages 571-581, September.

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