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Equivalent Representations of Set Functions

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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Michel Grabisch, Jean-Luc Marichal, Marc Roubens. Equivalent Representations of Set Functions. Mathematics of Operations Research, INFORMS, 2000, 25 (2), pp.157-178. ⟨10.1287/moor.⟩. ⟨hal-01194919⟩



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