A weight-based approach to the measurement of the interaction among criteria in the framework of aggregation by the bipolar Choquet integral

In the context of aggregation, the Choquet integral arises as a natural generalization of the weighted arithmetic mean. In their seminal work on bi-capacities, Grabisch and Labreuche have recently proposed an extension of the Choquet integral adapted to the situation where the values to be aggregated lie on a bipolar scale. In such a framework, they have derived generalizations of the Shapley value and of the Shapley interaction index that can be used to apprehend the main behavioral characteristics of the aggregation. Founding our approach on the intuitive notion of weight of a criterion, we propose alternative definitions of importance and interaction indices that may be more easily interpretable and we study their properties.