We present an alternative representation of seminormed integrals based on the t-cut of a monotone measure being a special level dependent Boolean capacity. We show that this representation is closely related to recently obtained transformation theorem for seminormed integrals. As a consequence we get a new characterization of Sugeno integral.

In this paper we study a generalization of a submeasure notion which is related to a probabilistic concept, especially to Menger spaces where triangular norms play a crucial role. The resulting notion of a τT-submeasure is suitable for modeling those situations in which we have only probabilistic information about the measure of the set. We characterize a class of universal τT-submeasures (i.e., τT-submeasures for an arbitrary t -norm T) and give explicit formulas for τT-submeasures for some classes of t -norms. Also, transformations and aggregations of τT-submeasures are discussed.