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Multiattribute preference models with reference points

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  • Denis Bouyssou

    () (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - CNRS - Centre National de la Recherche Scientifique)

  • Thierry Marchant

    () (Department of Data Analysis - UGENT - Ghent University [Belgium])

Abstract

In the context of multiple attribute decision making, preference models making use of reference points in an ordinal way have recently been introduced in the literature. This text proposes an axiomatic analysis of such models, with a particular emphasis on the case in which there is only one reference point. Our analysis uses a general conjoint measurement model resting on the study of traces induced on attributes by the preference relation and using conditions guaranteeing that these traces are complete. Models using reference points are shown to be a particular case of this general model. The number of reference points is linked to the number of equivalence classes distinguished by the traces. When there is only one reference point, the in- duced traces are quite rough, distinguishing at most two distinct equivalence classes. We study the relation between the model using a single reference point and other preference models proposed in the literature.

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  • Denis Bouyssou & Thierry Marchant, 2011. "Multiattribute preference models with reference points," Working Papers hal-00606942, HAL.
  • Handle: RePEc:hal:wpaper:hal-00606942
    Note: View the original document on HAL open archive server: https://hal.archives-ouvertes.fr/hal-00606942
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    References listed on IDEAS

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    1. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, I: The case of two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 217-245, April.
    2. Marichal, Jean-Luc & Roubens, Marc, 2000. "Determination of weights of interacting criteria from a reference set," European Journal of Operational Research, Elsevier, vol. 124(3), pages 641-650, August.
    3. Rolland, Antoine, 2013. "Reference-based preferences aggregation procedures in multi-criteria decision making," European Journal of Operational Research, Elsevier, vol. 225(3), pages 479-486.
    4. Bouyssou, Denis & Pirlot, Marc, 2005. "A characterization of concordance relations," European Journal of Operational Research, Elsevier, vol. 167(2), pages 427-443, December.
    5. Tversky, Amos & Kahneman, Daniel, 1992. "Advances in Prospect Theory: Cumulative Representation of Uncertainty," Journal of Risk and Uncertainty, Springer, vol. 5(4), pages 297-323, October.
    6. Bouyssou, Denis & Pirlot, Marc, 2005. "Following the traces:: An introduction to conjoint measurement without transitivity and additivity," European Journal of Operational Research, Elsevier, vol. 163(2), pages 287-337, June.
    7. Greco, Salvatore & Mousseau, Vincent & Slowinski, Roman, 2008. "Ordinal regression revisited: Multiple criteria ranking using a set of additive value functions," European Journal of Operational Research, Elsevier, vol. 191(2), pages 416-436, December.
    8. Kahneman, Daniel & Tversky, Amos, 1979. "Prospect Theory: An Analysis of Decision under Risk," Econometrica, Econometric Society, vol. 47(2), pages 263-291, March.
    9. Bouyssou, Denis & Marchant, Thierry, 2007. "An axiomatic approach to noncompensatory sorting methods in MCDM, II: More than two categories," European Journal of Operational Research, Elsevier, vol. 178(1), pages 246-276, April.
    10. Bouyssou, Denis & Pirlot, Marc, 2007. "Further results on concordance relations," European Journal of Operational Research, Elsevier, vol. 181(1), pages 505-514, August.
    11. Chateauneuf, Alain & Jaffray, Jean-Yves, 1989. "Some characterizations of lower probabilities and other monotone capacities through the use of Mobius inversion," Mathematical Social Sciences, Elsevier, vol. 17(3), pages 263-283, June.
    12. Greco, Salvatore & Matarazzo, Benedetto & Slowinski, Roman, 2004. "Axiomatic characterization of a general utility function and its particular cases in terms of conjoint measurement and rough-set decision rules," European Journal of Operational Research, Elsevier, vol. 158(2), pages 271-292, October.
    13. Fuad Aleskerov & Denis Bouyssou & Bernard Monjardet, 2007. "Utility Maximization, Choice and Preference," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00197186, HAL.
    14. Tversky, Amos & Kahneman, Daniel, 1986. "Rational Choice and the Framing of Decisions," The Journal of Business, University of Chicago Press, vol. 59(4), pages 251-278, October.
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    Cited by:

    1. Dias, Luis C. & Antunes, Carlos Henggeler & Dantas, Guilherme & de Castro, Nivalde & Zamboni, Lucca, 2018. "A multi-criteria approach to sort and rank policies based on Delphi qualitative assessments and ELECTRE TRI: The case of smart grids in Brazil," Omega, Elsevier, vol. 76(C), pages 100-111.
    2. 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.
    3. Christophe Labreuche & Michel Grabisch, 2018. "Using multiple reference levels in Multi-Criteria Decision aid: The Generalized-Additive Independence model and the Choquet integral approaches," Post-Print hal-02043265, HAL.
    4. Ferretti, Valentina & Liu, Jun & Mousseau, V & Ouerdane, W, 2017. "Reference-based ranking procedure for environmental decision making: insights from an ex-post analysis," LSE Research Online Documents on Economics 85933, London School of Economics and Political Science, LSE Library.
    5. Christophe Labreuche & Michel Grabisch, 2018. "Using multiple reference levels in Multi-Criteria Decision Aid: the Generalized-Additive Independence model and the Choquet integral approaches," Post-Print halshs-01815028, HAL.

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