On the solution of the fuzzy Sylvester matrix equation
In this paper, we consider the fuzzy Sylvester matrix equation \(AX+XB=C,\) where \(A\in {\mathbb{R}}^{n \times n}\) and \(B\in {\mathbb{R}}^{m \times m}\) are crisp M-matrices, C is an \(n\times m\) fuzzy matrix and X is unknown. We first transform this system to an \((mn)\times (mn)\) fuzzy system of linear equations. Then, we investigate the existence and uniqueness of a fuzzy solution to this system. We use the accelerated over-relaxation method to compute an approximate solution to this system. Some numerical experiments are given to illustrate the theoretical results.
fuzzy sylvester linear system of equations m-matrix aor