New solution principles of multi-criteria problems based on comparison standards

TL;DR

This paper introduces a novel formal method for solving extreme multi-criteria problems by transforming them into single-criterion models using comparison standards, ensuring Pareto-optimal solutions without extra information.

Contribution

It presents a new approach based on comparison standards and intervals, with proven Pareto-optimality and demonstrated effectiveness through examples.

Findings

Effective transformation of multi-criteria problems into single-criterion models.

Proof of Pareto-optimality of solutions.

Demonstrated efficiency and universality of the method.

Abstract

Proposed is a new formal approach for solution of extreme multi-criteria problems transforming them into single-criterion mathematical models, without any additional information. Transforming rules are based on comparison standards and intervals between these standards and goal function values, corresponding to problem solution. Pareto-optimality of these solutions is proved by a number of theorems. Examples illustrating efficiency and universality of this approach are presented.