Equivalent representations of set functions

Reference : Equivalent representations of set functions


	Document type :	Scientific journals : Article
	Discipline(s) :	Physical, chemical, mathematical & earth Sciences : Mathematics Business & economic sciences : Quantitative methods in economics & management
	To cite this reference:	http://hdl.handle.net/10993/1945

Title :	Equivalent representations of set functions
Language :	English
Author, co-author :	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]
Publication date :	May-2000
Journal title :	Mathematics of Operations Research
Publisher :	Institute for Operations Research (INFORMS)
Volume :	25
Issue/season :	2
Pages :	157-178
Peer reviewed :	Yes (verified by ORBi^lu)
Audience :	International
ISSN :	0364-765X
e-ISSN :	1526-5471
Keywords :	[en] set function ; pseudo-Boolean function ; Möbius inversion formula ; Shapley and Banzhaf values ; interaction indice ; game theory ; multicriteria decision making
Abstract :	[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.
Target :	Researchers ; Professionals ; Students
Permalink :	http://hdl.handle.net/10993/1945
DOI :	10.1287/moor.25.2.157.12225

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