Interval equations in problems of data processing
In the modeling of technical, economic, social systems, it is often necessary to solve equations with interval-specific parameters (interval equations). The solution of such equations requires special methods that differ from the methods for solving ordinary deterministic equations. A new method for solving interval equations based on the apparatus of interval mathematics is proposed. The aim of the study is to develop a completely formalized method for solving interval equations based on the mathematical apparatus thus mentioned. The method consists in using equivalent transformations of the both parts of the interval equation according to the laws of interval mathematics that allow one to move from the interval equation to the ordinary deterministic equations and their subsequent solution using known methods. It is shown that various interval equations can be solved using two different methods: multiple and interval methods. The differences between these two methods are revealed in the concept of solving the equation, in the mathematical apparatus thus used, in the possibility of exact solution, in the power of the resulting set of solutions. An example of solving the interval equation used in calculation of the contamination zone with a dangerous substance by two aforementioned methods is given. We develop a new approach to solving interval equations based on an equivalent transformation of the equation according to the laws of interval mathematics. Such a transformation allowed us to bring the equation to a deterministic form which makes it possible to solve it by well-known methods of solving ordinary (deterministic) equations. The developed approach provides the exact solution of the interval equation or its approximate solution (in the absence of exact solution).