Resolution of Fuzzy Relation Equations with Constraints
<p>This paper studies the resolution of the max-min compositional fuzzy relation equation with the constraint of <inline-formula id="M1"><math id="mathml_M1" display="inline" overflow="scroll"><munderover><mo movablelimits="fals...
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| Format: | Article |
| Language: | English |
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Tsinghua University Press
2023-09-01
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| Series: | Fuzzy Information and Engineering |
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| Online Access: | https://www.sciopen.com/article/10.26599/FIE.2023.9270017 |
| _version_ | 1797649168879058944 |
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| author | Xueyan Xu |
| author_facet | Xueyan Xu |
| author_sort | Xueyan Xu |
| collection | DOAJ |
| description | <p>This paper studies the resolution of the max-min compositional fuzzy relation equation with the constraint of <inline-formula id="M1"><math id="mathml_M1" display="inline" overflow="scroll"><munderover><mo movablelimits="false">∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mi>i</mi></msub></mrow></mrow><mo>=</mo><mn>1</mn></math></inline-formula>. The solvability and the unique solvability of this constrained fuzzy relation equation are characterized. Furthermore, this paper presents a resolution of it and designs a corresponding tabular method. Finally, a numerical example is provided to illustrate the resolution procedure.</p> |
| first_indexed | 2024-03-11T15:42:22Z |
| format | Article |
| id | doaj.art-a504b24eb79948bcafe359be80c80849 |
| institution | Directory Open Access Journal |
| issn | 1616-8658 1616-8666 |
| language | English |
| last_indexed | 2024-03-11T15:42:22Z |
| publishDate | 2023-09-01 |
| publisher | Tsinghua University Press |
| record_format | Article |
| series | Fuzzy Information and Engineering |
| spelling | doaj.art-a504b24eb79948bcafe359be80c808492023-10-26T10:31:37ZengTsinghua University PressFuzzy Information and Engineering1616-86581616-86662023-09-0115322023210.26599/FIE.2023.9270017Resolution of Fuzzy Relation Equations with ConstraintsXueyan Xu0School of Mathematical Sciences, Beijing Normal University, Beijing 100875, China<p>This paper studies the resolution of the max-min compositional fuzzy relation equation with the constraint of <inline-formula id="M1"><math id="mathml_M1" display="inline" overflow="scroll"><munderover><mo movablelimits="false">∑</mo><mrow class="MJX-TeXAtom-ORD"><mi>i</mi><mo>=</mo><mn>1</mn></mrow><mi>n</mi></munderover><mrow class="MJX-TeXAtom-ORD"><mrow class="MJX-TeXAtom-ORD"><msub><mi>x</mi><mi>i</mi></msub></mrow></mrow><mo>=</mo><mn>1</mn></math></inline-formula>. The solvability and the unique solvability of this constrained fuzzy relation equation are characterized. Furthermore, this paper presents a resolution of it and designs a corresponding tabular method. Finally, a numerical example is provided to illustrate the resolution procedure.</p>https://www.sciopen.com/article/10.26599/FIE.2023.9270017fuzzy relation equationfuzzy comprehensive evaluationconstraint condition |
| spellingShingle | Xueyan Xu Resolution of Fuzzy Relation Equations with Constraints Fuzzy Information and Engineering fuzzy relation equation fuzzy comprehensive evaluation constraint condition |
| title | Resolution of Fuzzy Relation Equations with Constraints |
| title_full | Resolution of Fuzzy Relation Equations with Constraints |
| title_fullStr | Resolution of Fuzzy Relation Equations with Constraints |
| title_full_unstemmed | Resolution of Fuzzy Relation Equations with Constraints |
| title_short | Resolution of Fuzzy Relation Equations with Constraints |
| title_sort | resolution of fuzzy relation equations with constraints |
| topic | fuzzy relation equation fuzzy comprehensive evaluation constraint condition |
| url | https://www.sciopen.com/article/10.26599/FIE.2023.9270017 |
| work_keys_str_mv | AT xueyanxu resolutionoffuzzyrelationequationswithconstraints |