Aggregation functions with non-monotonic measures

In this paper non-monotonic measures and their properties are considered and described. Subsequently we study discrete non-monotonic Choquet integral under the view- point of aggregation, and its axiomatic characterization. Moreover, we show that for non-monotonic measures the Shapley index can fail to represent the relative importance of a criterion, thus we introduce a new performance index. Finally we apply non-monotonic integral to a well known classical case study