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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 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique)

  • Christophe Labreuche

    () (UMP CNRS/THALES - Unité mixte de physique CNRS/Thalès - THALES - 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://halshs.archives-ouvertes.fr/halshs-00625706
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    References listed on IDEAS

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    Cited by:

    1. 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.
    2. 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.
    3. 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.
    4. 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.

    More about this item

    Keywords

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

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