NUMERICAL SOLUTION OF DUAL FUZZY SYLVESTER MATRIX EQUATIONS BY AN ITERATION METHOD

In this paper, dual fuzzy Sylvester matrix equations are studied for the first time. Two general approaches are presented to solve these equations. In the first approach, a dual fuzzy Sylvester matrix equation is transformed into a numeric linear system by Vec-operation and Kronecker product, where the dimension of the obtained system is much larger than the di-mension of original equation. In this reason, this method is not feasible for numerical solving of a dual fuzzy Sylvester matrix equation of a large dimension. In the second proposed approach, a dual fuzzy Sylvester matrix equation is transformed into two numeric Sylvester matrix equa-tions of the same dimensionality of the original problem. In the next step, a new iteration method is applied for solving the obtained numeric equations without using Vec-operation and Kronecker product. Finally, the efficiency and ability of the proposed method is illustrated by two numerical examples.