Models for Coordinated Integrated Assessment in Decision-Making Problems

Abstract

Introduction. The construction of a high-quality comprehensive assessment of an object requires a more accurate and comprehensive accounting of both objective information about the object, subjective assessments, individual experience, intuition and knowledge of the head of the object. Aim. The aim of the work is to develop a modern approach to solving the problems of multi-criteria assessment and ranking based on the formation of a coherent structure of an integrated assessment. To do this, a choice is made of the structure of the complex assessment system (a dichotomous tree, the hanging vertices of which correspond to the estimated directions and the root vertex corresponds to the complex assessment) and the matrix convolutions in each (non-hanging) tree vertex are selected. In addition, requirements are developed for grading scales, a convolution tree, and convolution matrices, which allow one to clearly demonstrate the synergistic effect and give a description of the class of generalized median schemes implemented on the convex representation of binary trees. Materials and methods. The solution to these problems is based on the method of synthesis and generalization of existing approaches to building a comprehensive assessment and simulation when choosing the structure of a complex assessment system. At the same time, convolution matrices are determined as training options set by experts, such that for any training option, the score obtained by the system of assessment coincides with the expert score. Results. The conditions for the existence of a matrix in the form of inequalities for generalized estimates of training sub-options are obtained. These inequalities are associated with a graph whose vertices denote sub-options, and arcs reflect inequalities connecting generalized estimates. It is shown that if the graph has no contours, then the convolution matrix exists. An algorithm is proposed for determining generalized estimates of sub variants based on the obtained graph and the subsequent determination of the corresponding matrix. The substantiation of the requirements for assessment scales and the structure of the convolution tree is given. The requirements are obtained for the dimension and type of convolution matrices located in the nodes of the tree. The possibility of implementing a set of training data using some kind of integrated assessment mechanism is determined. Conclusion. The results obtained make it possible to formulate integrated assessment systems that provide flexibility of tuning to the preferences of decision makers, ease of calculation, and the ability to solve optimization problems of program formation on this basis.