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Choquet integral calculus on a continuous support and its applications

Author

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  • Mustapha Ridaoui

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

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, PSE - Paris School of Economics - UP1 - Université Paris 1 Panthéon-Sorbonne - ENS-PSL - École normale supérieure - Paris - PSL - Université Paris Sciences et Lettres - EHESS - École des hautes études en sciences sociales - ENPC - École des Ponts ParisTech - CNRS - Centre National de la Recherche Scientifique - INRAE - Institut National de Recherche pour l’Agriculture, l’Alimentation et l’Environnement)

Abstract

In this paper, we give representation results about the calculation of the Choquet integral of a monotone function on the non negative real line. Next, we represent the Choquet integral of non monotone functions, by construction of monotone functions from non monotones ones, by using the increasing and decreasing rearrangement of a non monotone function. Finally, this paper is completed with some applications of these results to the continuous agregation operator OWA, and to the representation of risk measures by Choquet integral. .

Suggested Citation

  • Mustapha Ridaoui & Michel Grabisch, 2016. "Choquet integral calculus on a continuous support and its applications," Post-Print halshs-01411987, HAL.
    • Handle: RePEc:hal:journl:halshs-01411987
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01411987
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    References listed on IDEAS

    as
    1. Mario Ghossoub, 2015. "Equimeasurable Rearrangements with Capacities," Mathematics of Operations Research, INFORMS, vol. 40(2), pages 429-445, February.
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    3. Ulrich Faigle & Michel Grabisch, 2011. "A Discrete Choquet Integral for Ordered Systems," Post-Print halshs-00563926, HAL.
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    Cited by:

    1. Hamzeh Agahi, 2020. "On fractional continuous weighted OWA (FCWOWA) operator with applications," Annals of Operations Research, Springer, vol. 287(1), pages 1-10, April.
    2. 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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    More about this item

    Keywords

    Choquet integral; distorted Lebesgue measure; risk measure; OWA operator; intégrale de Choquet; mesure de Lebesgue distordue; mesure de risque; opérateur OWA;
    All these keywords.

    JEL classification:

    • C71 - Mathematical and Quantitative Methods - - Game Theory and Bargaining Theory - - - Cooperative Games

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