On distance distribution functions-valued submeasures related to   aggregation functions
  Probabilistic submeasures generalizing the classical (numerical) submeasures are introduced and discussed in connection with some classes of aggregation functions. A special attention is paid to triangular norm-based probabilistic submeasures and semi-copula-based probabilistic submeasures. Some algebraic properties of classes of such submeasures are also studied. 
Lenka Hal\v{c}inov\'a, Ondrej Hutn\'ik and Radko Mesiar
math.CA math.PR