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A representation of preferences by the Choquet integral with respect to a 2-additive capacity

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Abstract

In the context of Multiple criteria decision analysis, we present the necessary and sufficient conditions allowing to represent an ordinal preferential information provided by the decision maker by a Choquet integral w.r.t a 2-additive capacity. We provide also a characterization of this type of preferential information by a belief function which can be viewed as a capacity. These characterizations are based on three axioms, namely strict cycle-free preferences and some monotonicity conditions called MOPI and 2-MOPI.

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Authors and Affiliations

  1. Centre d’Economie de la Sorbonne, University of Paris I, 106-112 Boulevard de l’Hôpital, 75013, Paris, France

    Brice Mayag & Michel Grabisch

  2. Thales R & T, Campus de Polytechnique, 1 avenue Augustin Fresnel, 91767, Palaiseau cedex, France

    Brice Mayag & Christophe Labreuche

Authors
  1. Brice Mayag
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  2. Michel Grabisch
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  3. Christophe Labreuche
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Correspondence to Brice Mayag.

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Mayag, B., Grabisch, M. & Labreuche, C. A representation of preferences by the Choquet integral with respect to a 2-additive capacity. Theory Decis 71, 297–324 (2011). https://doi.org/10.1007/s11238-010-9198-3

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