Solution to equation in the interval arrangement
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 work is the development of a completely formalized method for solving interval equations based on the mathematical apparatus mentioned. The proposed method consists in using equivalent transformations of 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 by known methods. It is shown that the solution of various interval equations can be performed by two different methods: multiple and interval. The differences between these two methods in the concept of solving the equation, in the mathematical apparatus used, in the possibility of an exact solution, in the power of the resulting set of solutions are revealed. An example of a solution of the interval equation used in the calculation of the zone of contamination by a dangerous substance is given by two methods. The paper proposes 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 allows bring the equation to a deterministic form, which makes it possible to solve it by well-known methods for solving ordinary (deterministic) equations. The proposed approach allows us to find the exact solution of the interval equation (if it exists) or its approximate solution (if there is no exact solution).