Sugeno integrals with respect to level dependent capacities

The standard Sugeno integral has several equivalent ways to be introduced. This equivalence fails when generalizing the standard capacities into level dependent capacities. We discuss several possible types of Sugeno integral based on level dependent capacities. An illustrative example is added. Relations between different types of level dependent capacities-based Sugeno integrals are presented, showing that there are exactly three different types of studied integrals.