On the solution of a class of fuzzy system of linear equations

TL;DR

This paper investigates the existence and uniqueness of fuzzy solutions for linear systems where the coefficient matrix is a crisp H-matrix, extending results to M-matrices and diagonally dominant matrices, supported by numerical examples.

Contribution

It provides new theoretical conditions for the existence and uniqueness of fuzzy solutions in linear systems with H-matrices, M-matrices, and diagonally dominant matrices.

Findings

Established conditions for fuzzy solution existence and uniqueness.

Extended results to M-matrices and strictly diagonally dominant matrices.

Validated theoretical results with numerical examples.

Abstract

In this paper, we consider the system of linear equations $Ax=b$, where $A\in \Bbb{R}^{n \times n}$ is a crisp H-matrix and $b$ is a fuzzy $n$-vector. We then investigate the existence and uniqueness of a fuzzy solution to this system. The results can also be used for the class of M-matrices and strictly diagonally dominant matrices. Finally, some numerical examples are given to illustrate the presented theoretical results.