Analysis of functions which specified up to interval

The existing approaches to the calculation, analysis, synthesis and optimization of systems under conditions of uncertainty are considered. The problem of calculating and analyzing the behavior of is not fully determined function specified up to a range of possible values is formulated and described in detail. To solve this problem, an algorithm of determination is proposed, which reduces the problem to two similar problems - the upper and lower boundary functions of the original incompletely defined function. This algorithm uses means of interval mathematics and interval-differential calculus. We highlighted the different types of possible behavior of interval functions (consistency, increase, decrease, expansion, contraction) and various types of extreme points of these functions (the maximum point, minimum point, the point of maximum expansion, the point of minimum expansion). The theorems admitting to allocate areas in the different behavior of interval functions and points of their various extreme are proved. The execution of the proposed determination algorithm that allows to analyze the behavior of interval functions is described. This operation is illustrated in the specific example