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.

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