  Extending the idea of Even and Lehrer [3], we discuss a general approach to
integration based on a given decomposition system equipped with a weighting
function, and a decomposition of the integrated function. We distinguish two
type of decompositions: sub-decomposition based integrals (in economics linked
with optimization problems to maximize the possible profit) and
super-decomposition based integrals (linked with costs minimization). We
provide several examples (both theoretical and realistic) to stress that our
approach generalizes that of Even and Lehrer [3] and also covers problems of
linear programming and combinatorial optimization. Finally, we introduce some
new types of integrals related to optimization tasks.
