Resolution of linear interval systems using neural networks and their application to the Leontief economic model

Abstract

Linear systems with interval coefficients are a class of mathematical modeling problems whose coefficients do not have exact values, but are multi-valued sets of possible values. This feature characterizes many processes in the real world, especially in economics. The solution of these systems is essential for making decisions under uncertainty. In machine learning, neural networks represent an excellent tool for solving this problem. The performance of neural networks is largely due to their flexibility; they can learn multifaceted dependencies without any prior assumptions about the distribution of input data. In addition, it is important when the original data are measured inaccurately and/or noised. Such data are common in economic forecasting. In addition, their ability to learn data structures enables them to make accurate forecasts based on new data, which is decisive for risk management and strategic decision-making.One possibility is to model a concrete application on the Leontief model, which describes the flow between individual sectors of the economy. This way, when neural networks are integrated into linear systems with interval coefficients, it is possible to forecast the impact of variations in demand and supply over the whole economy, reducing the uncertainties of economic activity forecasts. In conclusion, the new methodology of neural networks in the resolution of linear systems with interval coefficients may, at some point, prove essential progress in managing economic uncertainty, allowing companies and decision-makers to navigate more confidently in a complex and unpredictable environment.