Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations
The fuzzy matrix equations A~⊗X~⊗B~=C~ in which A~, B~, and C~ are m×m, n×n, and m×n nonnegative LR fuzzy numbers matrices, respectively, are investigated. The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers...
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| Main Authors: | , |
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| Format: | Article |
| Language: | English |
| Published: |
Wiley
2013-01-01
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| Series: | Journal of Applied Mathematics |
| Online Access: | http://dx.doi.org/10.1155/2013/178209 |
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| _version_ | 1832568428169265152 |
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| author | Xiaobin Guo Dequan Shang |
| author_facet | Xiaobin Guo Dequan Shang |
| author_sort | Xiaobin Guo |
| collection | DOAJ |
| description | The fuzzy matrix equations A~⊗X~⊗B~=C~ in which A~, B~, and C~
are m×m, n×n, and m×n nonnegative LR fuzzy numbers matrices, respectively, are investigated.
The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to
arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate
solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. In addition,
the existence condition of nonnegative fuzzy solution is discussed. Two examples are calculated to
illustrate the proposed method. |
| format | Article |
| id | doaj-art-52b2091022bc4a2ca19e59bc695e071f |
| 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-52b2091022bc4a2ca19e59bc695e071f2025-02-03T00:59:07ZengWileyJournal of Applied Mathematics1110-757X1687-00422013-01-01201310.1155/2013/178209178209Fuzzy Approximate Solution of Positive Fully Fuzzy Linear 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 matrix equations A~⊗X~⊗B~=C~ in which A~, B~, and C~ are m×m, n×n, and m×n nonnegative LR fuzzy numbers matrices, respectively, are investigated. The fuzzy matrix systems is extended into three crisp systems of linear matrix equations according to arithmetic operations of LR fuzzy numbers. Based on pseudoinverse of matrix, the fuzzy approximate solution of original fuzzy systems is obtained by solving the crisp linear matrix systems. In addition, the existence condition of nonnegative fuzzy solution is discussed. Two examples are calculated to illustrate the proposed method.http://dx.doi.org/10.1155/2013/178209 |
| spellingShingle | Xiaobin Guo Dequan Shang Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations Journal of Applied Mathematics |
| title | Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations |
| title_full | Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations |
| title_fullStr | Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations |
| title_full_unstemmed | Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations |
| title_short | Fuzzy Approximate Solution of Positive Fully Fuzzy Linear Matrix Equations |
| title_sort | fuzzy approximate solution of positive fully fuzzy linear matrix equations |
| url | http://dx.doi.org/10.1155/2013/178209 |
| work_keys_str_mv | AT xiaobinguo fuzzyapproximatesolutionofpositivefullyfuzzylinearmatrixequations AT dequanshang fuzzyapproximatesolutionofpositivefullyfuzzylinearmatrixequations |