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Choquet integral calculus on a continuous support and its applications

Author

Listed:
  • 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 nationale des ponts et chaussées - 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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-01411987, HAL.
    • Handle: RePEc:hal:cesptp:halshs-01411987
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01411987v1
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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. Stanis{l}aw M. S. Halkiewicz, 2025. "NA-DiD: Extending Difference-in-Differences with Capabilities," Papers 2507.12690, arXiv.org, revised Dec 2025.
    3. 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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    JEL classification:

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

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