Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities
In this paper, we study a new type of fuzzy relation system called fuzzy relational inequalities with addition-min-product composition operations to model a peer-to-peer (P2P) file sharing system. Some properties of this addition-min-product system are investigated. We then characterize the structur...
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| Published in | Fuzzy optimization and decision making Vol. 21; no. 2; pp. 291 - 317 |
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| Main Authors | , |
| Format | Journal Article |
| Language | English |
| Published |
New York
Springer US
01.06.2022
Springer Nature B.V |
| Subjects | |
| Online Access | Get full text |
| ISSN | 1568-4539 1573-2908 |
| DOI | 10.1007/s10700-021-09368-7 |
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| Abstract | In this paper, we study a new type of fuzzy relation system called fuzzy relational inequalities with addition-min-product composition operations to model a peer-to-peer (P2P) file sharing system. Some properties of this addition-min-product system are investigated. We then characterize the structure of the solution set. Furthermore, to reduce the network congestion and improve the stability of data transmission, a min–max programming problem with constraints of addition-min-product fuzzy relation inequalities is established and investigated. We divide this min–max programming problem into several subproblems with the constraint of a single equation. Based on the optimal solutions to these subproblems, we can solve the original fuzzy relation min–max programming problem. Two algorithms, with polynomial computational complexity, are developed to search for an optimal solution to our studied problem. The validity of the algorithms is examined through a numerical example. |
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| AbstractList | In this paper, we study a new type of fuzzy relation system called fuzzy relational inequalities with addition-min-product composition operations to model a peer-to-peer (P2P) file sharing system. Some properties of this addition-min-product system are investigated. We then characterize the structure of the solution set. Furthermore, to reduce the network congestion and improve the stability of data transmission, a min–max programming problem with constraints of addition-min-product fuzzy relation inequalities is established and investigated. We divide this min–max programming problem into several subproblems with the constraint of a single equation. Based on the optimal solutions to these subproblems, we can solve the original fuzzy relation min–max programming problem. Two algorithms, with polynomial computational complexity, are developed to search for an optimal solution to our studied problem. The validity of the algorithms is examined through a numerical example. |
| Author | Yang, Xiaopeng Qiu, Jianjun |
| Author_xml | – sequence: 1 givenname: Jianjun surname: Qiu fullname: Qiu, Jianjun organization: School of Mathematics and Statistics, Lingnan Normal University – sequence: 2 givenname: Xiaopeng surname: Yang fullname: Yang, Xiaopeng email: happyyangxp@163.com organization: School of Mathematics and Statistics, Hanshan Normal University |
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| Cites_doi | 10.1016/j.fss.2017.04.002 10.1016/j.cie.2019.06.033 10.1109/ACCESS.2019.2958205 10.1016/j.asoc.2018.04.029 10.1016/S0165-0114(97)00184-X 10.1016/j.fss.2019.04.029 10.1007/s10700-008-9029-y 10.1016/j.ins.2011.03.004 10.1109/ACCESS.2020.2984095 10.1109/ACCESS.2018.2878748 10.1155/2019/4960638 10.1109/TFUZZ.2016.2598367 10.1142/S0218488519500247 10.1016/j.cam.2018.09.051 10.1109/TFUZZ.2015.2417593 10.1007/s10700-019-09306-8 10.1016/j.fss.2014.04.007 10.1016/j.cie.2014.03.024 10.1016/j.ins.2016.04.014 10.1016/j.fss.2017.08.001 10.1007/s10700-019-09305-9 10.1109/TFUZZ.2016.2593496 10.1109/FSKD.2012.6233956 |
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| Keywords | Min–max programming problem Fuzzy relation equation Addition-min-product composition Peer-to-Peer file sharing system Fuzzy relation inequality |
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| SubjectTerms | Algorithms Artificial Intelligence Calculus of Variations and Optimal Control; Optimization Data transmission Inequalities Mathematical Logic and Foundations Mathematics Mathematics and Statistics Operations Research/Decision Theory Optimization Polynomials Probability Theory and Stochastic Processes Programming |
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| Title | Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities |
| URI | https://link.springer.com/article/10.1007/s10700-021-09368-7 https://www.proquest.com/docview/2652409757 |
| Volume | 21 |
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