set function; pseudo-Boolean function; Möbius inversion formula; Shapley and Banzhaf values; interaction indice; game theory; multicriteria decision making
Résumé :
[en] This paper introduces four alternative representations of a set function: the Möbius transformation, the co-Möbius transformation, and the interactions between elements of any subset of a given set as extensions of Shapley and Banzhaf values. The links between the five equivalent representations of a set function are emphasized in this presentation.
Disciplines :
Mathématiques Méthodes quantitatives en économie & gestion
Identifiants :
UNILU:UL-ARTICLE-2010-377
Auteur, co-auteur :
Grabisch, Michel; University Pierre & Marie Curie (UPMC), Paris, France > LIP6
MARICHAL, Jean-Luc ; University of Liège, Belgium > Department of Management (FEGSS)
Roubens, Marc; University of Liège, Belgium > Institute of Mathematics
