Approximate Solution of LR Fuzzy Sylvester Matrix Equations
The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n 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 ext...
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| Format: | Article |
| Language: | English |
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Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/752760 |
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| _version_ | 1832547985446141952 |
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| author | Xiaobin Guo Dequan Shang |
| author_facet | Xiaobin Guo Dequan Shang |
| author_sort | Xiaobin Guo |
| collection | DOAJ |
| description | The fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n 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. |
| format | Article |
| id | doaj-art-51be2842bb1745a3a886348f77d39f84 |
| institution | Kabale University |
| issn | 1110-757X 1687-0042 |
| language | English |
| publishDate | 2013-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Journal of Applied Mathematics |
| spelling | doaj-art-51be2842bb1745a3a886348f77d39f842025-02-03T06:42:27ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/752760752760Approximate Solution of LR Fuzzy Sylvester Matrix EquationsXiaobin Guo0Dequan Shang1College of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaDepartment of Public Courses, Gansu College of Traditional Chinese Medicine, Lanzhou 730000, ChinaThe fuzzy Sylvester matrix equation AX~+X~B=C~ in which A,B are m×m and n×n crisp matrices, respectively, and C~ is an m×n 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.http://dx.doi.org/10.1155/2013/752760 |
| spellingShingle | Xiaobin Guo Dequan Shang Approximate Solution of LR Fuzzy Sylvester Matrix Equations Journal of Applied Mathematics |
| title | Approximate Solution of LR Fuzzy Sylvester Matrix Equations |
| title_full | Approximate Solution of LR Fuzzy Sylvester Matrix Equations |
| title_fullStr | Approximate Solution of LR Fuzzy Sylvester Matrix Equations |
| title_full_unstemmed | Approximate Solution of LR Fuzzy Sylvester Matrix Equations |
| title_short | Approximate Solution of LR Fuzzy Sylvester Matrix Equations |
| title_sort | approximate solution of lr fuzzy sylvester matrix equations |
| url | http://dx.doi.org/10.1155/2013/752760 |
| work_keys_str_mv | AT xiaobinguo approximatesolutionoflrfuzzysylvestermatrixequations AT dequanshang approximatesolutionoflrfuzzysylvestermatrixequations |