An axiomatic approach to the measurement of the amount of interaction among criteria or players

In the framework of multicriteria decision making based on fuzzy measures or cooperative game theory, an axiomatization of the concept of amount of interaction index is given. It is based on four axioms: a natural property called “absence of interaction”, a boundary condition for which the index reduces to the Shapley or Banzhaf interaction index, a pseudo-additivity axiom, and a recursivity property. The resulting index, which can be interpreted as a measure of the average degree of independence among criteria or players, takes a particularly simple and natural form for supermodular or submodular measures. The approach to the notion of interaction adopted in this paper can be seen as complementary to that recently adopted by Grabisch and Roubens.