On a Certain Class of submeasures Based on Triangular Norms

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.