Sugeno Integrals and the Commutation Problem

Didier Dubois (1, 2) , Hélène Fargier (1, 2) , Agnès Rico (3)

1 IRIT-ADRIA - Argumentation, Décision, Raisonnement, Incertitude et Apprentissage
2 CNRS - Centre National de la Recherche Scientifique
3 ERIC - Entrepôts, Représentation et Ingénierie des Connaissances

In decision problems involving two dimensions (like several agents and several criteria) the properties of expected utility ensure that the result of a multicriteria multiperson evaluation does not depend on the order with which the aggregations of local evaluations are performed (agents first, criteria next, or the converse). We say that the aggregations on each dimension commute. Ben Amor, Essghaier and Fargier have shown that this property holds when using pessimistic possibilistic integrals on each dimension, or optimistic ones, while it fails when using a pessimistic possibilistic integral on one dimension and an optimistic one on the other. This paper studies and completely solves this problem when Sugeno integrals are used in place of possibilistic integrals, indicating that there are capacities other than possibility and necessity measures that ensure commutation of Sugeno integrals.

Mots clés: Capacities; Sugeno integrals; Possibility theory; Commutation

Domaines: Mathématique discrète [cs.DM]; Informatique [cs]

Didier Dubois, Hélène Fargier, Agnès Rico. Sugeno Integrals and the Commutation Problem. 15th International Conference on Modeling Decisions for Artificial Intelligence (MDAI 2018), Oct 2018, Mallorca, Spain. pp.48-63, ⟨10.1007/978-3-030-00202-2_5⟩. ⟨hal-02053021⟩