Bi-capacities -- Part II: the Choquet integral

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dc.creatorGrabisch, Michel
dc.creatorLabreuche, Christophe
dc.date2007-11-14
dc.date.accessioned2026-07-07T08:42:51Z
dc.date.available2026-07-07T08:42:51Z
dc.descriptionBi-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.
dc.identifierhttps://arxiv.org/abs/0711.2112
dc.identifierhttp://arxiv.org/abs/0711.2112
dc.identifierFuzzy Sets and Systems (2005) 237-259
dc.identifier.urihttp://salesiana.dossiersoluciones.com/handle/123456789/142113
dc.subjectDiscrete Mathematics
dc.subjectComputer Science and Game Theory
dc.titleBi-capacities -- Part II: the Choquet integral
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