ВЕКТОРНАЯ МОДЕЛЬ МНОГОКРИТЕРИАЛЬНОЙ ОЦЕНКИ

Abstract

To assess the performance of economic systems, criteria and performance indicators are used that show the degree of achievement of the desired performance result. To characterize complex systems in most real cases, one criterion is not enough. Therefore, several criteria are used to comprehensively characterize the system. The multi-criteria problem raises the problem of matching individual criteria when used together. There are many ways to select alternatives in the face of multiple decision criteria. This article discusses the multi-criteria comparison of objects with Pareto dominance, vector estimates with arbitrary non-negative coordinates of vectors. The advantages of vector estimates in comparison with average estimates are considered. In this work, three important theorems of multi-criteria estimation are proved. The theorems define the conditions for the equivalence of three options for comparing objects by a variety of attributes: 1) arithmetic mean values; 2) the lengths of the corresponding vectors; 3) scalar products of vectors. As the research results, the application of the developed methods for aggregating the quality indicators of the educational process into a single assessment is shown. The following indicators of the educational process were used: coefficient of diligence, coefficient of interest, coefficient of difficulty of mastering the studied material, assessment of academic performance. A four-criteria optimization problem is formulated. It is shown that the objective function reaches its extreme value at the point that is as close as possible to the point of the optimal solution of the formulated problem. The issues of multi-criteria assessment developed in the article can find application in the management of the educational process in the formation of individual trajectories of trainees, in the tasks of working with the personnel of firms and organizations (selection, training, retraining), in assessing the quality of products and in other areas of activity.