Forms for calculation of universal coefficients when adopting multiple critical decisions

The problem of multi-criteria choice is a key element in making complex decisions. A number of methods have been proposed that suggest that decisions made with their use are the most rational. Their main element is the linear convolution of particular criteria, and the difference is in those or other heuristic or expert methods for specifying the numerical coefficients of the relative importance of the criteria. Previously, the author developed an approach that allows the use of pre-calculated universal tables of numerical coefficients of importance of particular criteria when forming a linear convolution. It significantly reduces both the laboriousness of the decision-making process and the inevitable subjectivity that arises during the heuristic selection or expert assignment of coefficients of importance. At the same time, the Monte-Carlo method was used for the calculation, which, in event of with a large number of criteria, created significant computational difficulties due to the lack of accuracy of the random number generator and the avalanche-like increase in the amount of computation. In this article, we managed to derive exact formulas for calculating universal importance coefficients. They are based on the so-called numerological approach, summarizing the patterns that emerged in the analysis of a number of tables of universal coefficients calculated by the statistical method. The formulas obtained allowed, in particular, the use of universal coefficients of importance of criteria in problems with any number of criteria, even without special software, which will contribute to the expansion of the scale of application of scientifically-based methods for making decisions.