Equivalent representations of set functions

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.

Disciplines :

Mathematics
Quantitative methods in economics & management

Identifiers :

UNILU:UL-ARTICLE-2010-377

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

Language :

English

Title :

Equivalent representations of set functions

Publication date :

May 2000

Journal title :

Mathematics of Operations Research

ISSN :

0364-765X

eISSN :

1526-5471

Publisher :

Institute for Operations Research (INFORMS)

Volume :

Issue :

Pages :

157-178

Peer reviewed :

Peer Reviewed verified by ORBi

Available on ORBilu :

since 22 May 2013

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