A generalization of universal integrals by means of level dependent capacities

An axiomatic approach to universal integrals based on level dependent capacities is presented. Based on a given semicopula, two corresponding extremal universal integrals based on level dependent capacities are given. If the underlying semicopula is even a copula, another class of universal integrals based on level dependent capacities is studied, generalizing, among others, both the Choquet and the Sugeno integral based on level dependent capacities which were introduced recently.