Copyright © 2013 Xiaobin Guo and Dequan Shang. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
The fuzzy Sylvester matrix equation in which are and crisp matrices, respectively, and is an LR fuzzy numbers matrix is investigated. Based on the Kronecker product of matrices,
we convert the fuzzy Sylvester matrix equation into an LR fuzzy linear system.
Then we extend the fuzzy linear system into two systems of linear equations according to the arithmetic operations of LR fuzzy numbers.
The fuzzy approximate solution of the original fuzzy matrix equation is obtained by solving the crisp linear systems.
The existence condition of the LR fuzzy solution is also discussed. Some examples are given to illustrate the proposed method.