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1 DECISION LIP6 - Laboratoire d-Informatique de Paris 6 2 CERMSEM - CEntre de Recherche en Mathématiques, Statistique et Économie Mathématique 3 Thales Research and Technology Palaiseau

Abstract : Bi-capacities arise as a natural generalization of capacities or fuzzy measures in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours, encompassing models such as Cumulative Prospect Theory CPT. The aim of this paper in two parts is to present the machinery behind bi-capacities, and thus remains on a rather theoretical level, although some parts are firmly rooted in decision theory, notably cooperative game theory. The present second part focuses on the definition of Choquet integral. We give several expressions of it, including an expression w.r.t. the Möbius transform. This permits to express the Choquet integral for 2-additive bi-capacities w.r.t. the interaction index.

Keywords : Choquet integral Bi-capacity Capacity Fuzzy measure

Autor: Michel Grabisch - Christophe Labreuche -



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