Perturbation Bounds of LR Fuzzy Linear Systems
This paper proposes a new method to discuss the perturbation problem of the LR fuzzy linear systems by an embedding method. By solving the perturbation equation of the original fuzzy linear systems, the respective relative error bounds are analyzed and obtained: (a) the right hand side is perturbed...
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2024-12-01
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| Series: | Fuzzy Information and Engineering |
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| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2024.9270049 |
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| _version_ | 1850072942398930944 |
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| author | Kun Liu Xiaobin Guo |
| author_facet | Kun Liu Xiaobin Guo |
| author_sort | Kun Liu |
| collection | DOAJ |
| description | This paper proposes a new method to discuss the perturbation problem of the LR fuzzy linear systems by an embedding method. By solving the perturbation equation of the original fuzzy linear systems, the respective relative error bounds are analyzed and obtained: (a) the right hand side is perturbed while the coefficient matrix remains unchanged; (b) the coefficient matrix is perturbed while the right hand side remains unchanged; and (c) both the coefficient matrix and the right hand side are perturbed. Some numerical examples are given to illustrated our proposed method. The results enrich the computation theories of fuzzy linear systems. |
| format | Article |
| id | doaj-art-1d357b76f73848a3ab2e4d94c9607bef |
| institution | DOAJ |
| issn | 1616-8658 1616-8666 |
| language | English |
| publishDate | 2024-12-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj-art-1d357b76f73848a3ab2e4d94c9607bef2025-08-20T02:46:59ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662024-12-0116433034510.26599/FIE.2024.9270049Perturbation Bounds of LR Fuzzy Linear SystemsKun Liu0Xiaobin Guo1School of Mathematics and Information Engineering, Longdong University, Qingyang 745000, ChinaCollege of Mathematics and Statistics, Northwest Normal University, Lanzhou 730070, ChinaThis paper proposes a new method to discuss the perturbation problem of the LR fuzzy linear systems by an embedding method. By solving the perturbation equation of the original fuzzy linear systems, the respective relative error bounds are analyzed and obtained: (a) the right hand side is perturbed while the coefficient matrix remains unchanged; (b) the coefficient matrix is perturbed while the right hand side remains unchanged; and (c) both the coefficient matrix and the right hand side are perturbed. Some numerical examples are given to illustrated our proposed method. The results enrich the computation theories of fuzzy linear systems.https://www.sciopen.com/article/10.26599/FIE.2024.9270049fuzzy numbersfuzzy linear systemmatrix normperturbation analysis |
| spellingShingle | Kun Liu Xiaobin Guo Perturbation Bounds of LR Fuzzy Linear Systems Fuzzy Information and Engineering fuzzy numbers fuzzy linear system matrix norm perturbation analysis |
| title | Perturbation Bounds of LR Fuzzy Linear Systems |
| title_full | Perturbation Bounds of LR Fuzzy Linear Systems |
| title_fullStr | Perturbation Bounds of LR Fuzzy Linear Systems |
| title_full_unstemmed | Perturbation Bounds of LR Fuzzy Linear Systems |
| title_short | Perturbation Bounds of LR Fuzzy Linear Systems |
| title_sort | perturbation bounds of lr fuzzy linear systems |
| topic | fuzzy numbers fuzzy linear system matrix norm perturbation analysis |
| url | https://www.sciopen.com/article/10.26599/FIE.2024.9270049 |
| work_keys_str_mv | AT kunliu perturbationboundsoflrfuzzylinearsystems AT xiaobinguo perturbationboundsoflrfuzzylinearsystems |