Mathematical Apparatus of Optimal Decision-Making Based on Vector Optimization

Mashunin Mashunin

doi:10.3390/asi2040032

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.

Highlights

The problem of making an optimal decision that meets the modern achievements of science and technology is connected, firstly, with the release of high-quality products, and, secondly, with the solution of problems of social and economic human development
The purpose of this work is to build a mathematical model for an object or system of decision making in the form of a vector problem of mathematical programming
The problem of adoption of the optimum decision in a difficult technical system based on some set of functional characteristics is one of the most important problems of system analysis and design

Summary

Introduction

The problem of making an optimal decision that meets the modern achievements of science and technology is connected, firstly, with the release of high-quality products, and, secondly, with the solution of problems of social and economic human development. The conditions of uncertainty are characterized by the fact that input data for decision-making, can be presented as random, fuzzy or incomplete data, [1,2,9,10]. Research on this problem of decision-making began with the work of Keeney and Raiffa [11]. The most common mathematical apparatus for model-based decision making is vector optimization [6,12,14,15,16,17,18,19]. Vector optimization is considered as a mathematical apparatus of a solution to the problem of acceptance of an optimal solution

Methods

Results

Discussion

Conclusion