Reference : Equivalent representations of set functions
Scientific journals : Article
Physical, chemical, mathematical & earth Sciences : Mathematics
Business & economic sciences : Quantitative methods in economics & management
http://hdl.handle.net/10993/1945
Equivalent representations of set functions
English
Grabisch, Michel mailto [University Pierre & Marie Curie (UPMC), Paris, France > LIP6]
Marichal, Jean-Luc mailto [University of Liège, Belgium > Department of Management (FEGSS)]
Roubens, Marc [University of Liège, Belgium > Institute of Mathematics]
May-2000
Mathematics of Operations Research
Institute for Operations Research (INFORMS)
25
2
157-178
Yes (verified by ORBilu)
International
0364-765X
1526-5471
[en] set function ; pseudo-Boolean function ; Möbius inversion formula ; Shapley and Banzhaf values ; interaction indice ; game theory ; multicriteria decision making
[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.
Researchers ; Professionals ; Students
http://hdl.handle.net/10993/1945
10.1287/moor.25.2.157.12225

File(s) associated to this reference

Fulltext file(s):

FileCommentaryVersionSizeAccess
Limited access
EquivalentSetFunctions.pdfNo commentaryAuthor postprint199.26 kBRequest a copy
Limited access
PV-EquivalentSetFunctions.pdfPublisher postprint729.1 kBRequest a copy

Bookmark and Share SFX Query

All documents in ORBilu are protected by a user license.