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


  • Michel Grabisch

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

  • Salvatore Greco

    (Faculty of Economics - Università degli studi di Catania [Catania])

  • Marc Pirlot

    (Faculté polytechnique de Mons - UMons - Université de Mons)


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," Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) halshs-00340374, HAL.
  • Handle: RePEc:hal:cesptp:halshs-00340374
    DOI: 10.1002/int.20301
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    References listed on IDEAS

    1. 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. 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.
    2. 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, Open Access Journal, vol. 10(4), pages 1-22, April.
    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.
    4. Salvatore Greco & Radko Mesiar & Fabio Rindone, 2016. "Generalized bipolar product and sum," Fuzzy Optimization and Decision Making, Springer, vol. 15(1), pages 21-31, March.


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