Equivalent Representations of Set Functions

Equivalent Representations of Set Functions

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...

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Veröffentlicht in:Mathematics of operations research 2000-05, Vol.25 (2), p.157-178
Hauptverfasser: Grabisch, Michel, Marichal, Jean-Luc, Roubens, Marc
Format: Artikel
Sprache:eng
Schlagworte:
Approximation
Computer Science
Dividends
Fractals
Game theory
Hammers
interaction indices
Mathematical functions
Mathematical models
Mathematical sets
Mathematical transformations
multicriteria decision making
Möbius inversion formula
Operations research
Polynomials
pseudo-Boolean function
Real numbers
Set function
Shapley and Banzhaf values
Studies
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Beschreibung
Zusammenfassung: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.
ISSN:0364-765X
1526-5471
DOI:10.1287/moor.25.2.157.12225