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Generalized Choquet-like aggregation functions for handling bipolar scales

Author

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  • 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)

  • Michel Grabisch

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

Abstract

We are interested in modeling interaction between criteria in Multi-Criteria Decision Making when underlying scales are bipolar. Interacting phenomena involving behavioral bias between attractive and repulsive values are in particular considered here. We show in an example that both the Choquet integral and the Cumulative Prospect Theory (CPT) model fail to represent these interacting phenomena. Axioms that enable the construction of the preferences of the decision maker over each attribute, and the representation of his preferences about aggregation of criteria are introduced and justified. We show there is a unique aggregation operator that fits with these axioms. It is based on the notion of {\em bi-capacity} and generalizes both the Choquet integral and the CPT model.

Suggested Citation

  • Christophe Labreuche & Michel Grabisch, 2006. "Generalized Choquet-like aggregation functions for handling bipolar scales," Post-Print halshs-00186907, HAL.
    • Handle: RePEc:hal:journl:halshs-00186907
    DOI: 10.1016/j.ejor.2004.11.008
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00186907
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    Cited by:

    1. Merad, Myriam & Dechy, Nicolas & Serir, Lisa & Grabisch, Michel & Marcel, Frédéric, 2013. "Using a multi-criteria decision aid methodology to implement sustainable development principles within an organization," European Journal of Operational Research, Elsevier, vol. 224(3), pages 603-613.
    2. Christophe Labreuche, 2018. "An axiomatization of the Choquet integral in the context of multiple criteria decision making without any commensurability assumption," Annals of Operations Research, Springer, vol. 271(2), pages 701-735, December.
    3. Michel Grabisch & Christophe Labreuche, 2010. "A decade of application of the Choquet and Sugeno integrals in multi-criteria decision aid," Annals of Operations Research, Springer, vol. 175(1), pages 247-286, March.
    4. Christophe Labreuche & Michel Grabisch, 2008. "A value for bi-cooperative games," Post-Print halshs-00308738, HAL.
    5. Christophe Labreuche & Michel Grabisch, 2016. "A comparison of the GAI model and the Choquet integral with respect to a k-ary capacity," Documents de travail du Centre d'Economie de la Sorbonne 16004, Université Panthéon-Sorbonne (Paris 1), Centre d'Economie de la Sorbonne.
    6. Labreuche, Christophe & Grabisch, Michel, 2018. "Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches," European Journal of Operational Research, Elsevier, vol. 267(2), pages 598-611.
    7. Nihad Aliyev, 2019. "Financial Markets with Multidimensional Uncertainty," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 2-2019, January-A.
    8. Kojadinovic, Ivan, 2007. "A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral," European Journal of Operational Research, Elsevier, vol. 179(2), pages 498-517, June.
    9. Nihad Aliyev & Xue-Zhong He, 2016. "Toward a General Model of Financial Markets," Research Paper Series 371, Quantitative Finance Research Centre, University of Technology, Sydney.
    10. Kojadinovic, Ivan & Marichal, Jean-Luc, 2007. "Entropy of bi-capacities," European Journal of Operational Research, Elsevier, vol. 178(1), pages 168-184, April.
    11. Greco, Salvatore & Mousseau, Vincent & Słowiński, Roman, 2014. "Robust ordinal regression for value functions handling interacting criteria," European Journal of Operational Research, Elsevier, vol. 239(3), pages 711-730.
    12. repec:hal:pseose:halshs-00752736 is not listed on IDEAS

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