Bases and transforms of set functions

Grabisch, Michel

Bases and transforms of set functions

Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) from HAL

Abstract: The paper studies the vector space of set functions on a finite set X, which can be alternatively seen as pseudo-Boolean functions, and including as a special cases games. We present several bases (unanimity games, Walsh and parity functions) and make an emphasis on the Fourier transform. Then we establish the basic duality between bases and invertible linear transform (e.g., the Möbius transform, the Fourier transform and interaction transforms). We apply it to solve the well-known inverse problem in cooperative game theory (find all games with same Shapley value), and to find various equivalent expressions of the Choquet integral.

Keywords: set function; basis; Walsh function; Fourier transform; game; fonction d'ensemble; base; fonction de Walsh; transformée de Fourier; jeu (search for similar items in EconPapers)
Date: 2015-05
New Economics Papers: this item is included in nep-gth
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01169287v1
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Published in 2015

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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:halshs-01169287

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