Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter
Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-paramet...
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| Main Authors: | , , , , |
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| Format: | Article |
| Language: | English |
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Wiley
2019-01-01
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| Series: | Complexity |
| Online Access: | http://dx.doi.org/10.1155/2019/8179763 |
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| author | Xiaobin Yang Haitao Lin Gang Xiao Huanbin Xue Xiaopeng Yang |
| author_facet | Xiaobin Yang Haitao Lin Gang Xiao Huanbin Xue Xiaopeng Yang |
| author_sort | Xiaobin Yang |
| collection | DOAJ |
| description | Considering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum (a∨b) and infimum (a∧b) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max-T fuzzy relation equations system. |
| format | Article |
| id | doaj-art-ca594b78e0aa453faa9e90db4fefe2f5 |
| institution | DOAJ |
| issn | 1076-2787 1099-0526 |
| language | English |
| publishDate | 2019-01-01 |
| publisher | Wiley |
| record_format | Article |
| series | Complexity |
| spelling | doaj-art-ca594b78e0aa453faa9e90db4fefe2f52025-08-20T03:24:03ZengWileyComplexity1076-27871099-05262019-01-01201910.1155/2019/81797638179763Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued ParameterXiaobin Yang0Haitao Lin1Gang Xiao2Huanbin Xue3Xiaopeng Yang4School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaSchool of Mathematics and Statistics, Hanshan Normal University, Chaozhou, Guangdong 521041, ChinaConsidering the application background on P2P network system, we investigate the max-product fuzzy relation equation with interval-valued parameter in this paper. Order relation on the set of all interval-valued numbers plays key role in the construction and resolution of the interval-valued-parameter fuzzy relation equation (IPFRE). The basic operations supremum (a∨b) and infimum (a∧b) in the IPFRE should be defined depending on the order relation. A novel total order is introduced for establishing the IPFRE. We also discuss some properties of the IPFRE system, including the consistency and structure of the complete solution set. Concepts of close index set and open index set are defined, helping us to construct the resolution method of the IPFRE system. We further provide a detailed algorithm for obtaining the complete solution set. Besides, the solution set is compared to that of the classical max-T fuzzy relation equations system.http://dx.doi.org/10.1155/2019/8179763 |
| spellingShingle | Xiaobin Yang Haitao Lin Gang Xiao Huanbin Xue Xiaopeng Yang Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter Complexity |
| title | Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter |
| title_full | Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter |
| title_fullStr | Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter |
| title_full_unstemmed | Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter |
| title_short | Resolution of Max-Product Fuzzy Relation Equation with Interval-Valued Parameter |
| title_sort | resolution of max product fuzzy relation equation with interval valued parameter |
| url | http://dx.doi.org/10.1155/2019/8179763 |
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