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Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches

Author

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  • Michel Grabisch

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

  • Salvatore Greco

    (Faculty of Economics - Unict - Università degli studi di Catania = University of Catania)

  • Marc Pirlot

    (Faculté polytechnique de Mons - UMONS - Université de Mons / University of Mons)

Abstract

Multi-criteria decision analysis studies decision problems in which the alternatives are evaluated on several dimensions or viewpoints. In the problems we consider in this paper, the scales used for assessing the alternatives with respect to a viewpoint are bipolar and univariate or unipolar and bivariate. In the former case, the scale is divided in two zones by a neutral point; a positive feeling is associated to the zone above the neutral point and a negative feeling to the zone below this point. On unipolar bivariate scales, an alternative can receive both a positive and a negative evaluation, reflecting contradictory feelings or stimuli. The paper discusses procedures and models that have been proposed to aggregate multi-criteria evaluations when the scale of each criterion is of one of the two types above. We present both a constructive and a descriptive view on this question; the descriptive approach is concerned with characterizations of models of preference, while the constructive approach aims at building preferences by questioning the decision maker. We show that these views are complementary.

Suggested Citation

  • Michel Grabisch & Salvatore Greco & Marc Pirlot, 2008. "Bipolar and bivariate models in multi-criteria decision analysis: descriptive and constructive approaches," Post-Print halshs-00340374, HAL.
    • Handle: RePEc:hal:journl:halshs-00340374
    DOI: 10.1002/int.20301
    Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-00340374
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    References listed on IDEAS

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    1. Grabisch, Michel & Labreuche, Christophe & Vansnick, Jean-Claude, 2003. "On the extension of pseudo-Boolean functions for the aggregation of interacting criteria," European Journal of Operational Research, Elsevier, vol. 148(1), pages 28-47, July.
    2. Vind, Karl, 1991. "Independent preferences," Journal of Mathematical Economics, Elsevier, vol. 20(1), pages 119-135.
    3. 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.
    4. Bouyssou, Denis, 1986. "Some remarks on the notion of compensation in MCDM," European Journal of Operational Research, Elsevier, vol. 26(1), pages 150-160, July.
    5. Peter E. Earl (ed.), 2001. "The Legacy of Herbert Simon in Economic Analysis," Books, Edward Elgar Publishing, volume 0, number 1201.
    6. Fishburn, Peter C., 1990. "Continuous nontransitive additive conjoint measurement," Mathematical Social Sciences, Elsevier, vol. 20(2), pages 165-193, October.
    7. Denis Bouyssou & Marc Pirlot, 2002. "Nontransitive Decomposable Conjoint Measurement," Post-Print hal-02361942, HAL.
    8. Michel Grabisch & Christophe Labreuche, 2016. "Fuzzy Measures and Integrals in MCDA," International Series in Operations Research & Management Science, in: Salvatore Greco & Matthias Ehrgott & José Rui Figueira (ed.), Multiple Criteria Decision Analysis, edition 2, chapter 0, pages 553-603, Springer.
    9. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    10. Fishburn, Peter C., 1990. "Additive non-transitive preferences," Economics Letters, Elsevier, vol. 34(4), pages 317-321, December.
    11. Denis Bouyssou & Marc Pirlot, 2004. "Preferences for multi-attributed alternatives: Traces, Dominance, and Numerical Representations," Post-Print hal-00004104, HAL.
    12. Christophe Labreuche & Michel Grabisch, 2003. "The Choquet integral for the aggregation of interval scales in multicriteria decision making," Post-Print hal-00272090, HAL.
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    Cited by:

    1. Wei Song & Zhiya Chen & Aijun Liu & Qiuyun Zhu & Wei Zhao & Sang-Bing Tsai & Hui Lu, 2018. "A Study on Green Supplier Selection in Dynamic Environment," Sustainability, MDPI, vol. 10(4), pages 1-22, April.
    2. 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.
    3. Javier Montero & Humberto Bustince & Camilo Franco & J. Tinguaro Rodríguez & Daniel Gómez & Miguel Pagola & Javier Fernandez & Edurne Barrenechea, 2014. "Paired structures and bipolar knowledge representation," MSAP Working Paper Series 06_2014, University of Copenhagen, Department of Food and Resource Economics.

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