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Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model

Author

Listed:
  • Paul Alain Kaldjob Kaldjob

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

  • Brice Mayag

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

  • Denis Bouyssou

    (LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision - Université Paris Dauphine-PSL - PSL - Université Paris sciences et lettres - CNRS - Centre National de la Recherche Scientifique)

Abstract

This paper proposes and studies the notion of interaction between two criteria in a 2-maxitive Sugeno integral model. Within the framework of binary alternatives, we give a necessary and sufficient condition for preferential information on binary alternatives to be representable by a 2-maxitive Sugeno integral model. Using this condition, we show that it is always possible to choose a numerical representation, for which all the interaction indices are strictly positive. Outside the framework of binary alternatives, by introducing binary variables, we propose a MILP allowing to test whether an ordinal preference information is representable by a 2-maxitive Sugeno integral model and whether the interpretation of the interaction indices is ambiguous or not. We illustrate our results with examples.

Suggested Citation

  • Paul Alain Kaldjob Kaldjob & Brice Mayag & Denis Bouyssou, 2021. "Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model," Post-Print halshs-03483960, HAL.
    • Handle: RePEc:hal:journl:halshs-03483960
    DOI: 10.1007/978-3-030-87756-9_21
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