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

Galand, Lucie; Mayag, Brice (2017), A Heuristic Approach to Test the Compatibility of a Preference Information with a Choquet Integral Model, in Rothe, Jörg, Algorithmic Decision Theory: 5th International Conference, ADT 2017, Springer International Publishing : Cham, p. 65-80. 10.1007/978-3-319-67504-6_5

Type
Communication / Conférence
Date
2017
Conference title
5th International Conference (ADT 2017)
Conference date
2017-10
Conference city
Luxembourg
Conference country
Luxembourg
Book title
Algorithmic Decision Theory: 5th International Conference, ADT 2017
Book author
Rothe, Jörg
Publisher
Springer International Publishing
Published in
Cham
ISBN
978-3-319-67503-9; 978-3-319-67504-6
Number of pages
390
Pages
65-80
Publication identifier
10.1007/978-3-319-67504-6_5
Metadata
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Author(s)
Galand, Lucie
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Mayag, Brice
Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)
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.
Subjects / Keywords
MCDA; Preference modeling; Choquet integral; interaction

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