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A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity

Author

Listed:
  • Brice Mayag

    (LGI - Laboratoire Génie Industriel - EA 2606 - CentraleSupélec)

  • 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 allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

Suggested Citation

  • Brice Mayag & Michel Grabisch & Christophe Labreuche, 2011. "A Representation of Preferences by the Choquet Integral with Respect to a 2-Additive Capacity," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00625706, HAL.
    • Handle: RePEc:hal:cesptp:halshs-00625706
    DOI: 10.1007/s11238-010-9198-3
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00625706
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    Cited by:

    1. Mayag, Brice & Bouyssou, Denis, 2020. "Necessary and possible interaction between criteria in a 2-additive Choquet integral model," European Journal of Operational Research, Elsevier, vol. 283(1), pages 308-320.
    2. Paul Alain Kaldjob Kaldjob & Brice Mayag & Denis Bouyssou, 2023. "On the interpretation of the interaction index between criteria in a Choquet integral model," Post-Print hal-03766372, HAL.
    3. Sébastien Courtin & Rodrigue Tido Takeng & Frédéric Chantreuil, 2020. "Decomposition of interaction indices: alternative interpretations of cardinal-probabilistic interaction indices ," Working Papers hal-02952516, HAL.
    4. 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.
    5. Paul Alain Kaldjob Kaldjob & Brice Mayag & Denis Bouyssou, 2022. "On the robustness of the sign of nonadditivity index in a Choquet integral model," Post-Print hal-03904424, HAL.
    6. 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.
    7. Axel C. Mühlbacher & Anika Kaczynski, 2016. "Making Good Decisions in Healthcare with Multi-Criteria Decision Analysis: The Use, Current Research and Future Development of MCDA," Applied Health Economics and Health Policy, Springer, vol. 14(1), pages 29-40, February.
    8. Ferreira, João J.M. & Jalali, Marjan S. & Ferreira, Fernando A.F., 2018. "Enhancing the decision-making virtuous cycle of ethical banking practices using the Choquet integral," Journal of Business Research, Elsevier, vol. 88(C), pages 492-497.
    9. 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.
    10. Serena Doria, 2019. "Preference orderings represented by coherent upper and lower conditional previsions," Theory and Decision, Springer, vol. 87(2), pages 233-252, September.
    11. 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).
    12. 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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    Keywords

    multicriteria decision making; Choquet integral; 2-additive capacity; MACBETH;
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