A method for solving fuzzy matrix equations

There are many reported studies, in which researchers tried to solve a system of fuzzy linear equations numerically. In this paper, a numerical method for solving fuzzy system A X ~ B = C ~ of matrix equations is investigated. As it can be observed in the form of these equations, the unknown matrix X , which is the solution to these equations, has a left-hand coefficient matrix A and a right-hand coefficient matrix B . Such character makes these equations different from other equations in the form of A X ~ = B ~ . In the aforesaid equations, A and B are crisp matrices and C ~ and X ~ are matrices with fuzzy arrays. In this work using the parametric form of fuzzy linear equations and presenting an algorithm, two systems of equations will be developed and solved afterward. A comparison of the number of multiplications in this method with a different one will be drawn afterward. Some numerical examples are given to illustrate the effectiveness of the proposed method.