Interaction transform for bi-set functions over a finite set

Fabien Lange () and Michel Grabisch
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Fabien Lange: CES - Centre d'économie de la Sorbonne - UP1 - Université Paris 1 Panthéon-Sorbonne - CNRS - Centre National de la Recherche Scientifique

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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.

Keywords: Set function; Bi-set function; Möbius transform; Interaction transform (search for similar items in EconPapers)
Date: 2006-08
Note: View the original document on HAL open archive server: https://hal.science/hal-00186891
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Published in Information Sciences, 2006, 176 (16), pp.2279-2303. ⟨10.1016/j.ins.2005.10.004⟩

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Working Paper: Interaction transform for bi-set functions over a finite set (2006)
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Persistent link: https://EconPapers.repec.org/RePEc:hal:cesptp:hal-00186891

DOI: 10.1016/j.ins.2005.10.004

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