2 research outputs found
An integral with respect to probabilistic-valued decomposable measures
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.Comment: 17 pages, 2 metapost figures; v2 substantially rewritten version
including application to Moore's interval analysis, 19 pages, 2 metapost
figure
Probabilistic-valued decomposable set functions with respect to triangle functions
In the framework of the generalized measure theory the decomposable
probabilistic-valued set functions are introduced with triangle functions
in an appropriate probabilistic metric space as natural candidates for
the "addition", leading to the concept of -decomposable measures. Several
set functions, among them the classical (sub)measures, previously defined
-submeasures, -submeasures as well as recently introduced
Shen's (sub)measures are described and investigated in a unified way. Basic
properties and characterizations of -decomposable (sub)measures are also
studied and numerous extensions of results from the above mentioned papers are
provided.Comment: v2 rewritten substantially, 14 page