Construction of a nonlinear convolution of particular efficiency criteria in the vector optimization problem

Abstract

The paper considers methods for constructing linear and nonlinear convolutions of particular criteria (indicators) of the efficiency of the functioning of the objects under study. In the second case, the problem of choosing the best transformation for each such criterion is solved, selected from a set of such transformations, which are, among other things, elementary functions. The developed algorithms are based on the use of both information about the values of the criteria for each object, and specially formed expert information. The latter has a «soft» character and concerns only the fixation of the fact of either equal or higher efficiency of functioning of one object in relation to another, without any quantitative assessment of the degree of such excess. And only later, within the framework of the proposed algorithm, this essentially qualitative information acquires a partly quantitative character. Cases of consistent and contradictory expert information are considered for both linear and nonlinear convolutions. For the first of them, the objective function of the generated linear programming problem is the maximization of the resolving power of the system of linear inequalities; in the second, it is the minimization of the total distortions introduced into the system of constraints to ensure its compatibility. This technique is used in the theory of solving ill-posed problems and is based on the definition of their so-called quasisolutions. When choosing the best transformation for each particular criterion, it is proposed to solve linear-Boolean programming problems.