Integrated Assessment System Based on Dichotomous Tree

Abstract

To assess the state of complex objects (regions, enterprises, programs, etc.), integrated assessment systems (IA) based on dichotomous trees and matrix convolution of assessment criteria are currently widely used. The dichotomous tree determines the structure of the IA-system (the order of convolution of criteria), and the matrix convolutions at the vertices of the tree determine the generalized estimates obtained as a result of the convolution of two estimates. The task of synthesizing an IA-system includes determining the structure of the system (dichotomous tree) and convolution matrices at each vertex of the tree, with the exception of the initial. The second problem is considered in the article, i.e. convolution matrix determination problems based on training options set by experts. The task is to determine (m − 1) matrices, where m – is the number of criteria so that for any training option, the score obtained on the basis of the IA-system coincides with the expert one. The problem is considered for the case of a consistent tree structure, when the criteria are added one at a time (criteria 1 and 2 are aggregated, criterion 3 is added to the resulting generalized estimate, etc.). The idea of the proposed approach consists in the sequential construction of convolution matrices, starting from the top level, the next matrix is built on the basis of the previous one. At the same time, the conditions for the existence of a matrix in the form of inequalities for generalized estimates of learning sub-options are obtained. These inequalities are associated with a graph whose vertices denote subvariants, and arcs reflect inequalities connecting generalized estimates.