Bi-capacities -- Part I: definition, Möbius transform and interaction - Université Paris 1 Panthéon-Sorbonne Accéder directement au contenu
Article Dans Une Revue Fuzzy Sets and Systems Année : 2005

Bi-capacities -- Part I: definition, Möbius transform and interaction

Résumé

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 first part is devoted to the introduction of bi-capacities and the structure on which they are defined. We define the Möbius transform of bi-capacities, by just applying the well known theory of M\" obius functions as established by Rota to the particular case of bi-capacities. Then, we introduce derivatives of bi-capacities, by analogy with what was done for pseudo-Boolean functions (another view of capacities and set functions), and this is the key point to introduce the Shapley value and the interaction index for bi-capacities. Thi is done in a cooperative game theoretic perspective. In summary, all familiar notions used for fuzzy measures are available in this more general framework.
Fichier principal
Vignette du fichier
fss04I.pdf (279.75 Ko) Télécharger le fichier
Origine : Fichiers produits par l'(les) auteur(s)

Dates et versions

hal-00187189 , version 1 (13-11-2007)

Identifiants

Citer

Michel Grabisch, Christophe Labreuche. Bi-capacities -- Part I: definition, Möbius transform and interaction. Fuzzy Sets and Systems, 2005, 151 (2), pp.211-236. ⟨10.1016/j.fss.2004.08.012⟩. ⟨hal-00187189⟩
156 Consultations
525 Téléchargements

Altmetric

Partager

Gmail Facebook X LinkedIn More