Solving Large Scale System of Fuzzy Linear Equations Based on Multi-Objective Optimization Technique

Document Type : Original Article

Authors

1 Mathematics Department, Faculty of Science, South Valley University, Qena 83523, Egypt

2 Mathematics Department, Faculty of Science, Assuit University, Assuit 81111, Egypt

Abstract

This paper considers solving a large-scale system of fuzzy linear equations that arise in various applications such as supply chain, transport, and networks (water, electricity, and gas), etc. The significance of applications containing ambiguous data necessitates the development of methodologies to address it. Such type of problem cannot be solved accurately by the analytical methods or the classical numerical iterative method. Here we will adapt a technique that transforms the fuzzy linear system into a multi-objective optimization problem. Then the obtained multi-objective optimization problem will be transformed into a single objective optimization problem. The Leap Frog method is one of the head methods that are used to solve single optimization problems. It will be introduced as a part of the introduced technique for solving the obtained single optimization problem. The convexity and the convergence for the approach and the Leap Frog method will be present. Some test examples are introduced to ensure the accuracy of the proposed approach.

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