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A characterization of the 2-additive Choquet integral through cardinal information

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  • Brice Mayag

    (CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique, Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - 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)

  • Christophe Labreuche

    (Laboratoire Albert Fert (ex-UMPhy Unité mixte de physique CNRS/Thales) - THALES [France] - Université Paris-Saclay - CNRS - Centre National de la Recherche Scientifique)

Abstract

In the context of multiple criteria decision analysis, we present the necessary and sufficient conditions to represent a cardinal preferential information by the Choquet integral w.r.t. a 2-additive capacity. These conditions are based on some complex cycles called cyclones.
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Suggested Citation

  • 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.
    • Handle: RePEc:hal:cesptp:halshs-00445132
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    2. Beliakov, Gleb, 2022. "Knapsack problems with dependencies through non-additive measures and Choquet integral," European Journal of Operational Research, Elsevier, vol. 301(1), pages 277-286.
    3. Li, Jianping & Yao, Xiaoyang & Sun, Xiaolei & Wu, Dengsheng, 2018. "Determining the fuzzy measures in multiple criteria decision aiding from the tolerance perspective," European Journal of Operational Research, Elsevier, vol. 264(2), pages 428-439.
    4. Silvia Bortot & Ricardo Alberto Marques Pereira & Thuy H. Nguyen, 2015. "Welfare functions and inequality indices in the binomial decomposition of OWA functions," DEM Discussion Papers 2015/08, Department of Economics and Management.
    5. Alessio Bonetti & Silvia Bortot & Mario Fedrizzi & Silvio Giove & Ricardo Alberto Marques Pereira & Andrea Molinari, 2011. "Modelling group processes and effort estimation in Project Management using the Choquet integral: an MCDM approach," DISA Working Papers 2011/12, Department of Computer and Management Sciences, University of Trento, Italy, revised Sep 2011.
    6. Kadaifci, Cigdem & Asan, Umut & Bozdag, Erhan, 2020. "A new 2-additive Choquet integral based approach to qualitative cross-impact analysis considering interaction effects," Technological Forecasting and Social Change, Elsevier, vol. 158(C).
    7. Kadaifci, Cigdem, 2024. "A new approach to MACTOR considering interaction effects: An example from the telecommunications industry in Turkey," Technological Forecasting and Social Change, Elsevier, vol. 209(C).
    8. Silvia Bortot & Ricardo Alberto Marques Pereira, 2011. "Inconsistency and non-additive Choquet integration in the Analytic Hierarchy Process," DISA Working Papers 2011/06, Department of Computer and Management Sciences, University of Trento, Italy, revised 29 Jul 2011.

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