Approximate solution of dual fuzzy matrix equations

In this paper, we propose a simple and practical method to solve the dual fuzzy matrix equation Ax̃+B∼=Cx̃+D∼, in which A,CA,C are m×nm×n matrices and B∼,D∼ are m×pm×p LR fuzzy numbers matrices. By means of the arithmetic operations on LR fuzzy numbers space, the dual fuzzy matrix equation could be converted into two classical matrix equations, and the LR minimal fuzzy solution and the strong (weak) LR minimal fuzzy solutions of the dual fuzzy matrix equation are derived by solving two classical matrix equations based on the generalized inverses of matrices. Meanwhile, as a special case of the dual fuzzy matrix equation, the fuzzy solutions of the dual fuzzy linear systems are investigated. Finally, some numerical examples are given to illustrate the effectiveness of the proposed method.