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A Heuristic Approach to Test the Compatibility of a Preference Information with a Choquet Integral Model

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Algorithmic Decision Theory (ADT 2017)

Part of the book series: Lecture Notes in Computer Science ((LNAI,volume 10576))

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Abstract

This work deals with the problem of the existence of a Multicriteria Decision Aiding model, based on the Choquet integral, that represents the preferences of a decision maker. Given some preferences on a set of actions, our aim is to determine if those preferences are compatible with a Choquet integral model, where the utility function associated to each criterion and the capacity on the subsets of criteria are to be defined. Computing simultaneously the utility functions and the capacity leads to solving a mixed integer program with some quadratic constraints, which can not be performed efficiently. We propose here to solve this problem by using a linear approximation of the quadratic terms given by the Taylor’s formula, and then apply a standard mixed integer programming solver. We illustrate and analyze our approach with some numerical experiments.

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Notes

  1. 1.

    A binary action is a fictitious alternative which takes either the neutral value \(\mathbf {0}\) for all criteria, or the neutral value \(\mathbf {0}\) for all criteria except for one or two criteria for which it takes the satisfactory value \(\mathbf {1}\). The binary actions are used in many applications through the MACBETH methodology [3, 5].

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Authors and Affiliations

  1. University Paris-Dauphine, PSL Research University LAMSADE, CNRS, UMR 7243, Place du Maréchal de Lattre de Tassigny, 75775, Paris Cedex 16, France

    Lucie Galand & Brice Mayag

Authors
  1. Lucie Galand
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  2. Brice Mayag
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Corresponding author

Correspondence to Brice Mayag .

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Editors and Affiliations

  1. Heinrich Heine University, Düsseldorf, Germany

    Jörg Rothe

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Galand, L., Mayag, B. (2017). A Heuristic Approach to Test the Compatibility of a Preference Information with a Choquet Integral Model. In: Rothe, J. (eds) Algorithmic Decision Theory. ADT 2017. Lecture Notes in Computer Science(), vol 10576. Springer, Cham. https://doi.org/10.1007/978-3-319-67504-6_5

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  • DOI: https://doi.org/10.1007/978-3-319-67504-6_5

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  • Publisher Name: Springer, Cham

  • Print ISBN: 978-3-319-67503-9

  • Online ISBN: 978-3-319-67504-6

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