Reduction of the Pareto Set in Multicriteria Economic Problem with CES Functions

TL;DR

This paper presents a method to reduce the Pareto set in a multicriteria economic problem with CES functions by incorporating fuzzy preferences, resulting in a narrower set of optimal solutions.

Contribution

It introduces a novel approach to Pareto set reduction using fuzzy preferences and axiomatic methods for problems with CES production functions.

Findings

Constructs an upper bound of the optimal set within the Pareto set.

Applies fuzzy preferences to refine resource allocation solutions.

Demonstrates the reduction process through solving three crisp multicriteria problems.

Abstract

A multicriteria economic problem is considered: the basic production assets and the labor resources define a set of feasible solutions (alternatives), labor costs, costs of the basic production assets (to be minimized), and cost of the manufactured products (to be maximized) are objective functions. The production function with constant elasticity of substitution is used. The decision maker's (DM's) preferences are introduced as follows: lower labor costs and costs of the basic production assets have the greater importance than higher income, and vice a versa. The fuzzy preferences along with the compromise have a degree of its confidence. Such crisp and fuzzy information is applied in the axiomatic approach of the Pareto set reduction by V. D. Noghin. We show how to construct a set, which is an upper bound of the optimal choice and belongs to the Pareto set of the problem in crisp and fuzzy cases. In fuzzy case one should solve a three crisp multicriteria problems. Thus, upon the crisp and fuzzy DM's preferences a narrower upper bounds of the optimal set of resources with respect to criteria and additional information are obtained.