Bases and transforms of set functions

Grabisch, Michel

Bases and transforms of set functions

Abstract: The chapter 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: basis; set functions; TU games; Fourier transform; Möbius transform; interaction Shapley value; Choquet integral; bases; fonctions d'ensemble; jeux TU; transformée de Fourier; transformée de Möbius; interaction valeur Shapley; intégrale de Choquet (search for similar items in EconPapers)
Date: 2016-11
Note: View the original document on HAL open archive server: https://shs.hal.science/halshs-01411966v1
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Published in 2016

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Persistent link: https://EconPapers.repec.org/RePEc:hal:journl:halshs-01411966

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