MATHEMATICAL METHODS APPLICATION IN SYSTEM ANALYSIS FOR DECISION-MAKING IN THE EDUCATIONAL PROCESS

Modern education is characterized by a high level of uncertainty and dynamism, which requires the educators ability to make informed decisions in limited information conditions. Mathematical methods of system analysis are applied in the research to optimize the decision-making process in the educational environment. One of the models in the educational process for the description and analysis of various aspects of the educational process, such as the motivation of the participants of the educational process, the quality of educational services, is considered. The search for optimal solutions in conditions of uncertainty for the processing of inaccurate and incomplete information, which is typical for the educational environment, was carried out. The algorithm of the decision-making process under uncertainty conditions is described. The problem of finding the optimal solution in conditions of uncertainty is considered using the example of one model of promoting an educational service with various modifications of the risk matrix. Optimal solutions were found using the Bayes criteria, the minimum variance of the estimated functional with its modifications, the maximizing the probability distribution of an estimated functional, the modal criterion, the minimum entropy, and the combined criterion. The results of calculations for decision-making according to various criteria in the conditions of uncertainty are obtained for various risk matrix modifications. Relevant conclusions were drawn. The study results can be used to optimize educational programs and teaching methods, improve the quality of educational services, increase the motivation of the educational process participants and more effectively use educational resources. The obtained results are useful for researchers and practitioners who are dealing with decisionmaking problems under uncertainty in various fields.