How do we digitize the concept of "more important"

The problem of multi-criteria analysis is a key element in making complex decisions, retaining its relevance for over fifty years. A number of decision-making approaches and methods, allowing assumption of rationality of their results, have been proposed over the years. The main idea behind the majority of those methods is the linear convolution of partial criterions and the main difference lies in heuristic or expert methods, implicated in numerical expression of weight coefficients of the criteria. In light of this, it seems beneficial to find universal means of multi-criterion comparison of alternatives, based on a small number of natural axioms that are strictly mathematically sound and, at the same time, simple in practical application. The paper proposes an approach based on a transition from continuous space of weight coefficients of partial criterions importance towards a discreet space of behavior methods that is more natural for the decision-maker. This transition enabled a relatively simple classification of decision-making tasks and made possible to form a universal table of relative weights of partial criterions, applicable to any task of multi-criteria optimization on a set of alternatives. In addition, several new aspects of comparative analysis of multi-criteria alternatives were considered based on the analysis of the concept of “importance”. In particular, the invalidity of averaging of normalized criteria values, considered to be of equivalent importance had been shown; also, the so-called “edge effect” which consists in the constancy of the chains of relative importance coefficients of criteria that meet the same extreme fragments of the decision-making policy. A comparative analysis of the proposed method with the well-known method of analytic hierarchy, proposed by Thomas Saaty was carried out and a modification, allowing to increase the ease of use and validity of this method, was developed.