Interaction transform for bi-set functions over a finite set

Authors:
Fabien Lange;Michel Grabisch
Affiliations:
Université Paris I - Panthéon-Sorbonne CERMSEM, 106-112 bd de l'Hôpital, 75013 Paris, France;Université Paris I - Panthéon-Sorbonne CERMSEM, 106-112 bd de l'Hôpital, 75013 Paris, France and Université Paris I - Panthéon-Sorbonne LIP6, 8 rue du Capitaine Scott, 750 ...
Venue:
Information Sciences: an International Journal
Year:
2006

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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 Mobius 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.