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Advances in Fuzzy Systems
Volume 2012, Article ID 318069, 9 pages
Research Article

Fuzzy Symmetric Solutions of Fuzzy Matrix Equations

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

Received 3 April 2012; Accepted 29 April 2012

Academic Editor: F. Herrera

Copyright © 2012 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 symmetric solution of fuzzy matrix equation AX˜=B˜, in which A is a crisp m×m nonsingular matrix and B˜ is an m×n fuzzy numbers matrix with nonzero spreads, is investigated. The fuzzy matrix equation is converted to a fuzzy system of linear equations according to the Kronecker product of matrices. From solving the fuzzy linear system, three types of fuzzy symmetric solutions of the fuzzy matrix equation are derived. Finally, two examples are given to illustrate the proposed method.