Equivalent Representations of Set Functions

Michel Grabisch
Michel Grabisch
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LIP6, University Pierre & Marie Curie (UPMC), 8, rue du Capitaine Scott, 75015 Paris, France
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Jean-Luc Marichal
Jean-Luc Marichal
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Department of Management, FEGSS, University of Liège, Boulevard du Rectorat 7—B31, B-4000 Liège, Belgium
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Marc Roubens
Marc Roubens
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Institute of Mathematics, University of Liège, Grande Traverse 12—B37, Campus du Sart Tilman, B-4000 Liège, Belgium
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Michel Grabisch

[email protected]

LIP6, University Pierre & Marie Curie (UPMC), 8, rue du Capitaine Scott, 75015 Paris, France

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Jean-Luc Marichal

[email protected]

Department of Management, FEGSS, University of Liège, Boulevard du Rectorat 7—B31, B-4000 Liège, Belgium

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Marc Roubens

[email protected]

Institute of Mathematics, University of Liège, Grande Traverse 12—B37, Campus du Sart Tilman, B-4000 Liège, Belgium

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Published Online:1 May 2000https://doi.org/10.1287/moor.25.2.157.12225

Abstract

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.

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cover image Mathematics of Operations Research

Volume 25, Issue 2

May 2000

Pages 157-347

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Received:May 03, 1999
Published Online:May 01, 2000

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Michel Grabisch, Jean-Luc Marichal, Marc Roubens, (2000) Equivalent Representations of Set Functions. Mathematics of Operations Research 25(2):157-178.

https://doi.org/10.1287/moor.25.2.157.12225

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Equivalent Representations of Set Functions

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