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Choquet integral with respect to a symmetric fuzzy measure of a function on the real line

Author

Listed:
  • Yasuo Narukawa

    (Toho Gakuen
    Tokyo Institute of Technology)

  • Vicenç Torra

    (IIIA—CSIC)

  • Michio Sugeno

    (European Centre for Soft Computing)

Abstract

Some results about the calculation of the Choquet integral of a monotone function are presented. The construction of monotone functions from non-monotone ones that lead to the same Choquet integral is studied. The paper is completed with the application of these results to the continuous WOWA operator, as well as with some differential equations also applied to the determination of the weight in this operator.

Suggested Citation

  • 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.
    • Handle: RePEc:spr:annopr:v:244:y:2016:i:2:d:10.1007_s10479-012-1166-6
    DOI: 10.1007/s10479-012-1166-6
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    References listed on IDEAS

    as
    1. Itzhak Gilboa & David Schmeidler, 1992. "Additive Representation of Non-Additive Measures and the Choquet Integral," Discussion Papers 985, Northwestern University, Center for Mathematical Studies in Economics and Management Science.
    2. 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.
    3. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Post-Print halshs-00563926, HAL.
    4. Michel Grabisch & Jean-Luc Marichal & Radko Mesiar & Endre Pap, 2009. "Aggregation functions," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00445120, HAL.
    5. Pedro Miranda & Michel Grabisch & Pedro Gil, 2002. "p-symmetric fuzzy measures," Post-Print hal-00273960, HAL.
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    Cited by:

    1. Torra, Vicenç, 2023. "The transport problem for non-additive measures," European Journal of Operational Research, Elsevier, vol. 311(2), pages 679-689.
    2. LeSheng Jin & Radko Mesiar & Martin Kalina & Ronald R. Yager, 2020. "Canonical form of ordered weighted averaging operators," Annals of Operations Research, Springer, vol. 295(2), pages 605-631, December.
    3. Hamzeh Agahi, 2020. "On fractional continuous weighted OWA (FCWOWA) operator with applications," Annals of Operations Research, Springer, vol. 287(1), pages 1-10, April.
    4. Negi, Shekhar Singh & Torra, Vicenç, 2022. "Δ-Choquet integral on time scales with applications," Chaos, Solitons & Fractals, Elsevier, vol. 157(C).

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