A novel technique to solve the fuzzy system of equations

TL;DR

This paper introduces a new embedding-based technique for efficiently solving fuzzy linear systems by transforming them into crisp systems, improving upon existing methods and demonstrating its effectiveness through algorithms and examples.

Contribution

It presents a modified and improved embedding method for solving FSLEs, reducing computational operations compared to prior methods, with practical algorithms and illustrative examples.

Findings

The proposed method reduces the number of operations needed.

Solutions are obtained in fuzzy form, preserving fuzziness.

Algorithms successfully solve example FSLEs.

Abstract

The aim of this research is to apply a novel technique based on the embedding method to solve the n*n fuzzy system of linear equations (FSLEs). By using this method, the strong fuzzy number solutions of FSLEs can be obtained by transforming the n*n FSLE to the crisp system. In this paper, Ezzati's method to solve the FSLEs is modified and improved. Several theorems are proved to show the number of operations for presented method are less than the methods of Friedman and Ezzati. In order to show the advantages of scheme, two applicable algorithms are presented and several examples are solved by applying them. Also, some graphs of obtained results are demonstrated which show the solutions are in the fuzzy form.