Journal of Applied Mathematics
Volume 2013 (2013), Article ID 752760, 10 pages
http://dx.doi.org/10.1155/2013/752760
Research Article

Approximate Solution of LR Fuzzy Sylvester Matrix Equations

Xiaobin Guo1 and Dequan Shang2

1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, China
2Department of Public Courses, Gansu College of Traditional Chinese Medicine, Lanzhou 730000, China

Received 4 September 2012; Revised 17 October 2012; Accepted 5 November 2012

Academic Editor: Hector Pomares

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.

Abstract

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.