Identification of a 2-Additive Bi-Capacity by Using Mathematical Programming

Julien Ah-Pine (1) , Brice Mayag (2) , Antoine Rolland (1)

1 ERIC - Entrepôts, Représentation et Ingénierie des Connaissances
2 LAMSADE - Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision

In some multi-criteria decision making problems, it is more convenient to express the decision maker preferences in bipolar scales. In such cases, the bipolar Choquet integral with respect to bi-capacities was introduced. In this paper, we address the problem of eliciting a bipo-lar Choquet integral with respect to a 2-additive bi-capacity. We assume that we are given a set of examples with (i) their scores distribution in regard to several criteria and (ii) their overall scores. We propose two types of optimization problems that allow identifying the parameters of a 2-additive bi-capacity such that the inferred bipolar Choquet integral is consistent with the given examples as much as possible. Furthermore, since the elicitation process we study has many relationships with problems in statistical machine learning, we also present the links between our models and concepts developed in the latter field.

Mots clés: 2-additive bi-capacity identification; Bipolar Choquet integral; Preference elicitation

Domaines: Intelligence artificielle [cs.AI]; Recherche opérationnelle [math.OC]; Apprentissage [cs.LG]

Julien Ah-Pine, Brice Mayag, Antoine Rolland. Identification of a 2-Additive Bi-Capacity by Using Mathematical Programming. Third International Conference on Algorithmic Decision Theory (ADT 2013), Nov 2013, Bruxelles, Belgium. pp.15-29, ⟨10.1007/978-3-642-41575-3_2⟩. ⟨hal-01504630⟩