Interaction transform for bi-set functions over a finite set

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Interaction transform for bi-set functions over a finite set

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Michel Grabisch () (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)
Fabien Lange (CES - Centre d'économie de la Sorbonne - CNRS : UMR8174 - Université Panthéon-Sorbonne - Paris I)

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Abstract

Set functions appear as a useful tool in many areas of decision making and operations research, and several linear invertible transformations have been introduced for set functions, such as the Möbius transform and the interaction transform. The present paper establish similar transforms and their relationships for bi-set functions, i.e. functions of two disjoint subsets. Bi-set functions have been recently introduced in decision making (bi-capacities) and game theory (bi-cooperative games), and appear to open new areas in these fields.

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Paper provided by HAL in its series Université Paris1 Panthéon-Sorbonne (Post-Print and Working Papers) with number hal-00186891_v1.

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Date of creation: Aug 2006
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Publication status: Published, Information Sciences, 2006, 176, 16, 2279-2303
Handle: RePEc:hal:cesptp:hal-00186891_v1

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Michel Grabisch & Christophe Labreuche, 2002. "The Symmetric and Asymmetric Choquet integrals on finite spaces fordecision making," Post-Print halshs-00273184_v1, HAL. [Downloadable!]
Other versions:
- Michel Grabisch & Christophe Labreuche, 2002. "The symmetric and asymmetric Choquet integrals on finite spaces for decision making," Statistical Papers, Springer, vol. 43(1), pages 37-52, January. [Downloadable!] (restricted)

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