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

Paul Alain Kaldjob Kaldjob, Brice Mayag () and Denis Bouyssou
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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

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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.

Keywords: Binary alternatives; Sugeno integral model; Interaction indices; 2-maxitive capacity (search for similar items in EconPapers)
Date: 2021-10-27
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Published in Algorithmic Decision Theory, 13023, Springer International Publishing, pp.323-337, 2021, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-87756-9_21⟩

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-03483960

DOI: 10.1007/978-3-030-87756-9_21

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