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


Author Info

  • Michel Grabisch

    (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Paris I - Panthéon-Sorbonne)

  • Salvatore Greco

    (Faculty of Economics - University of Catania)

  • Marc Pirlot

    (Faculté polytechnique de Mons - Polytechnic College of 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.

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Bibliographic Info

Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number halshs-00340374.

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Date of creation: Sep 2008
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Publication status: Published, International Journal of Intelligent Systems, 2008, 23, 9, 930-969
Handle: RePEc:hal:cesptp:halshs-00340374

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Keywords: Multiple criteria; Decision analysis; Preference; Bipolarmodels; Choquet integral;


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  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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