New axiomatizations of the Shapley interaction index for bi-capacities

Authors:
Fabien Lange;Michel Grabisch
Affiliations:
Óbuda University, Keleti Faculty of Business and Management, Tavaszmező utca 15-17, 1084 Budapest, Hungary;Centre d'Économie de la Sorbonne, Université Paris I - Panthéon-Sorbonne, 106-112 bd de l'Hôpital, 75013 Paris, France
Venue:
Fuzzy Sets and Systems
Year:
2011

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Abstract

Bi-capacities are a natural generalization of capacities (or fuzzy measures) in a context of decision making where underlying scales are bipolar. They are able to capture a wide variety of decision behaviours. After a short presentation of the basis structure, we introduce the Shapley value and the interaction index for capacities. Afterwards, the case of bi-capacities is studied with new axiomatizations of the interaction index.