Mathematical Apparatus of Optimal Decision-Making Based on Vector Optimization

Abstract

We present a problem of “acceptance of an optimal solution” as a mathematical model in the form of a vector problem of mathematical programming. For the solution of such a class of problems, we show the theory of vector optimization as a mathematical apparatus of acceptance of optimal solutions. Methods of solution of vector problems are directed to problem solving with equivalent criteria and with the given priority of a criterion. Following our research, the analysis and problem definition of decision making under the conditions of certainty and uncertainty are presented. We show the transformation of a mathematical model under the conditions of uncertainty into a model under the conditions of certainty. We present problems of acceptance of an optimal solution under the conditions of uncertainty with data that are represented by up to four parameters, and also show geometrical interpretation of results of the decision. Each numerical example includes input data (requirement specification) for modeling, transformation of a mathematical model under the conditions of uncertainty into a model under the conditions of certainty, making optimal decisions with equivalent criteria (solving a numerical model), and, making an optimal decision with a given priority criterion.