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Chapitre d'ouvrage Année : 2021

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

Résumé

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.
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Dates et versions

halshs-03483960, version 1 (16-12-2021)

Identifiants

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Paul Alain Kaldjob Kaldjob, Brice Mayag, Denis Bouyssou. Necessary and Possible Interaction in a 2-Maxitive Sugeno Integral Model. Algorithmic Decision Theory, 13023, Springer International Publishing, pp.323-337, 2021, Lecture Notes in Computer Science, ⟨10.1007/978-3-030-87756-9_21⟩. ⟨halshs-03483960⟩
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