We can stress three main problems which usually occurs in complex modeling:
uncertainty, nonlinearity and optimization.
We can usually describe these models with same nonlinear equations (ordinary differential , difference , partial differential, optimization, etc.). Different kinds of nonlinear equations are treated in mathematics with many different tools. We shall briefly present a mathematical background for treating all three mentioned problems. The base of our approach will be a class of non-additive measures so called null-additive set functions and integrals based on them. We are using also Choquet and Sugeno integrals ( [9], [6],[27], (341) . Special attention will be taken on so called pseudo-addition decomposable measures. Namely, instead of the usual plus-product structure of real numbers a semiring structure on extended reals with respect to some other operations (pseudmperations) is considered. For example, max-min, max-plus, max-product or operations generated by some additive generator g are included, and specially triangular conorm-triangular norm (151, [S], [ll], [13]). There were developed some parts of mathematical analysis in analogy with the classical mathematical analysis as for example measure theory, integration, integral operators, convolution, delta-sequences, Laplace transform, etc. ([21] -