New axiomatizations of the Shapley interaction index for bi-capacities

Fabien Lange (1) , Michel Grabisch (2)

1 Keleti Faculty of Economics
2 CES - Centre d'économie de la Sorbonne

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.

Domaines: Mathématique discrète [cs.DM]; Economies et finances; Informatique et théorie des jeux [cs.GT]; Recherche opérationnelle [math.OC]

Fabien Lange, Michel Grabisch. New axiomatizations of the Shapley interaction index for bi-capacities. Fuzzy Sets and Systems, 2011, pp.64-75. ⟨hal-00625355⟩