Identification of a 2-Additive Bi-Capacity by Using Mathematical Programming
Ah-Pine, Julien; Mayag, Brice; Rolland, Antoine (2013), Identification of a 2-Additive Bi-Capacity by Using Mathematical Programming, in Perny, Patrice; Pirlot, Marc; Tsoukias, Alexis, Algorithmic Decision Theory, Springer-Verlag Berlin : Heidelberg, p. 15-29. 10.1007/978-3-642-41575-3_2
TypeCommunication / Conférence
Conference titleThird International Conference, ADT 2013
Book titleAlgorithmic Decision Theory
Book authorPerny, Patrice; Pirlot, Marc; Tsoukias, Alexis
Number of pages442
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Laboratoire d'analyse et modélisation de systèmes pour l'aide à la décision [LAMSADE]
Abstract (EN)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 bipolar 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.
Subjects / Keywords2-additive bi-capacity identification; Bipolar Choquet integral; Preference elicitation
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