On Non-monotonic Choquet integrals as Aggregation Functions

This paper deals with non-monotonic Choquet integral, a generalization of the regular Choquet integral. The discrete non-monotonic Choquet integral is considered under the viewpoint of aggregation. In particular we give an axiomatic characterization of the class of non-monotonic Choquet integrals.We show how the Shapley index, in contrast with the monotonic case, can assume positive values if the criterion is in average a benefit, depending on its effect in all the possible coalition coalitions, and negative values in the opposite case of a cost criterion.