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The problem of multi-criteria choice is a key element in making complex decisions and it has not lost its relevance for more than half a century. A number of approaches and methods suggest that the decisions made with their use are most rational. An overview of the most common methods and their applications is presented. The main element of most of these methods is the linear convolution of particular criteria, and their difference consists in one or another heuristic or expert way of specifying the numerical coefficients of the importance of the criteria. Author developed an approach that allows the pre-calculated universal tables of numerical coefficients of the importance of particular criteria to be used in the formation of a linear convolution, which significantly reduces both the complexity of the decision-making process and the inevitable subjectivism arising from heuristic selection or expert assignment of its coefficients. In the paper, an analogous approach is developed for an equally theoretically and practically important convolution of criteria, which in different publications is called differently: minimax, guarantee, Hermieier convolution. This allowed us to propose a new general method for making decisions and comparing multicriteria alternatives (the MUC method), based on the joint use of both types of bundles. Its application was demonstrated on two practically important tasks - the rating evaluation of universities and the analysis of various design concepts of high-altitude unmanned aero vehicles.