Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities
In this study, a BitTorrent-like peer-to-peer (BT-P2P) file-sharing system is reduced into a system of fuzzy relational inequalities (FRI) with addition-min composition. To study the stability of data transmission and network congestion, a min-max programming problem subject to addition-min FRI is p...
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| Published in | Fuzzy optimization and decision making Vol. 21; no. 3; pp. 429 - 454 |
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| Main Authors | , , , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.09.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1568-4539 1573-2908 |
| DOI | 10.1007/s10700-021-09371-y |
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| Abstract | In this study, a BitTorrent-like peer-to-peer (BT-P2P) file-sharing system is reduced into a system of fuzzy relational inequalities (FRI) with addition-min composition. To study the stability of data transmission and network congestion, a min-max programming problem subject to addition-min FRI is proposed. From a cost-saving perspective, the optimal solution to the min-max programming problem may not be the minimal optimal solution. Furthermore, while the “optimal” solution provides better cost performance, the “minimal” solution provides for the least congestion of the file-sharing system. In this paper, we propose adopting a binding variable approach based on certain new theoretical properties to find a minimal optimal solution for the min-max programming problem. It is for these new properties that the minimal optimal solution obtained via the binding variable approach would minimize the maximum transmission level; further, the amounts of data download in the optimal solution would be as balanced as possible. Some numerical examples are provided after each of the new properties to illustrate the advantages of our approach. |
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| AbstractList | In this study, a BitTorrent-like peer-to-peer (BT-P2P) file-sharing system is reduced into a system of fuzzy relational inequalities (FRI) with addition-min composition. To study the stability of data transmission and network congestion, a min-max programming problem subject to addition-min FRI is proposed. From a cost-saving perspective, the optimal solution to the min-max programming problem may not be the minimal optimal solution. Furthermore, while the “optimal” solution provides better cost performance, the “minimal” solution provides for the least congestion of the file-sharing system. In this paper, we propose adopting a binding variable approach based on certain new theoretical properties to find a minimal optimal solution for the min-max programming problem. It is for these new properties that the minimal optimal solution obtained via the binding variable approach would minimize the maximum transmission level; further, the amounts of data download in the optimal solution would be as balanced as possible. Some numerical examples are provided after each of the new properties to illustrate the advantages of our approach. |
| Author | Hsu, Yuan-Teng Wang, Ming-Xian Wu, Yan-Kuen Wen, Ching-Feng |
| Author_xml | – sequence: 1 givenname: Yan-Kuen orcidid: 0000-0001-7788-8157 surname: Wu fullname: Wu, Yan-Kuen email: ykwvnu@gmail.com organization: School of International Business, Shaoxing Key Laboratory of Intelligent Monitoring and Prevention of Smart City, Zhejiang Yuexiu University of Foreign Languages – sequence: 2 givenname: Ching-Feng surname: Wen fullname: Wen, Ching-Feng email: cfwen@kmu.edu.tw organization: Center for Fundamental Science and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Department of Medical Research, Kaohsiung Medical University Hospital – sequence: 3 givenname: Yuan-Teng surname: Hsu fullname: Hsu, Yuan-Teng organization: Research Center of Finance, Shanghai Business School – sequence: 4 givenname: Ming-Xian surname: Wang fullname: Wang, Ming-Xian organization: School of International Business, Zhejiang Yuexiu University of Foreign Languages |
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| CitedBy_id | crossref_primary_10_1109_TFUZZ_2024_3514746 crossref_primary_10_3934_math_2024665 crossref_primary_10_1109_TFUZZ_2023_3284392 crossref_primary_10_1016_j_fss_2025_109369 crossref_primary_10_1016_j_fss_2024_109011 crossref_primary_10_1109_ACCESS_2024_3467191 crossref_primary_10_1016_j_fss_2025_109363 |
| Cites_doi | 10.1109/ACCESS.2020.2984095 10.1109/TFUZZ.2016.2598367 10.1007/s10700-019-09305-9 10.1016/j.fss.2014.04.007 10.1016/j.jfranklin.2019.02.007 10.1016/j.ins.2016.04.014 10.1007/s10700-008-9029-y 10.1109/TFUZZ.2017.2648864 10.1016/j.fss.2017.08.001 10.1007/978-94-017-1650-5 10.1023/A:1022848114005 10.1016/j.fss.2017.04.002 10.1109/TFUZZ.2016.2593496 10.1007/s40815-018-0530-3 10.1007/s13042-016-0527-x 10.1016/0165-0114(82)90043-4 10.1007/978-3-642-04576-9_6 10.1016/j.ins.2020.03.047 10.1109/TFUZZ.2015.2428716 10.1109/TFUZZ.2017.2771406 10.1109/FSKD.2012.6233956 10.1007/978-3-319-46206-6_48 |
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| Keywords | Min-max programming problem Addition-min fuzzy relational inequality Minimal optimal solution |
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| SubjectTerms | Artificial Intelligence Binding Calculus of Variations and Optimal Control; Optimization Congestion Data transmission Downloading File sharing Inequalities Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Peer to peer computing Probability Theory and Stochastic Processes Programming |
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| Title | Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities |
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