The solution of fuzzy Sylvester matrix equation

In this paper, A fuzzy Sylvester matrix equation with crisp coefficient matrices is considered. We use the arithmetic operation rule of fuzzy number to transfer the equation into two crisp Sylvester matrix equations, which avoids using Kronecker operation and which makes it possible to apply some existing methods to solve Sylvester matrix equation. Since the two transferred equations keep the number of unknowns unchanged, numerical operations needed in our method are much less than the operations in the method using Kronecker product. At last, we use several small-scale examples to illustrate the correctness of our method and several large-scale examples to illustrate the efficiency of our method.