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...