Generalizing Choquet integral with level dependent capacities

We present a generalization of Choquet integral in which the capacity depends on the level of the aggregated variables. We show that as particular cases of our generalization of Choquet integral there are the Sugeno integral, the Sipos integral and the Cumulative Prospect Theory functional. We show also that many concepts such as Mobius transform, importance index, interaction index, k-order capacities and OWA operators, introduced in the research about Choquet integral can be generalized in the considered context