  Several concepts of approximate reasoning in uncertainty processing are
linked to the processing of distribution functions. In this paper we make use
of probabilistic framework of approximate reasoning by proposing a
Lebesgue-type approach to integration of non-negative real-valued functions
with respect to probabilistic-valued decomposable (sub)measures. Basic
properties of the corresponding probabilistic integral are investigated in
detail. It is shown that certain properties, among them linearity and
additivity, depend on the properties of the underlying triangle function
providing (sub)additivity condition of the considered (sub)measure. It is
demonstrated that the introduced integral brings a new tool in approximate
reasoning and uncertainty processing with possible applications in several
areas.
