A fast algorithm for the linear programming problem constrained with the Weighted power mean-Fuzzy Relational Equalities (WPM-FRE)

TL;DR

This paper introduces a fast algorithm for solving linear programming problems constrained by a specific fuzzy relational equality involving weighted power mean, with theoretical analysis and procedures for simplification and solution.

Contribution

The paper develops a novel algorithm for linear programming with WPM-FRE constraints, including theoretical properties, feasibility conditions, and simplification procedures.

Findings

Derived properties of the feasible region.

Necessary and sufficient conditions for feasibility.

An illustrative example demonstrating the algorithm.

Abstract

In this paper, a linear programming problem is investigated in which the feasible region is formed as a special type of fuzzy relational equalities (FRE). In this type of FRE, fuzzy composition is considered as the weighted power mean operator (WPM). Some theoretical properties of the feasible region are derived and some necessary and sufficient conditions are also presented to determine the feasibility of the problem. Moreover, two procedures are proposed for simplifying the problem. Based on some structural properties of the problem, an algorithm is presented to find the optimal solutions and finally, an example is described to illustrate the algorithm.