Max-min fuzzy bi-level programming: resource sharing system with application
This study delves into the application of min-max fuzzy relation systems, specifically focusing on equality and inequality, in the examination of educational institution networks and their resource-sharing dynamics, akin to a P2P network structure. Expanding upon this framework, this article intrica...
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| Published in | Applied mathematics in science and engineering Vol. 32; no. 1 |
|---|---|
| Main Author | |
| Format | Journal Article |
| Language | English |
| Published |
Abingdon
Taylor & Francis Ltd
31.12.2024
Taylor & Francis Group |
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| Abstract | This study delves into the application of min-max fuzzy relation systems, specifically focusing on equality and inequality, in the examination of educational institution networks and their resource-sharing dynamics, akin to a P2P network structure. Expanding upon this framework, this article intricately explores a mathematical system featuring three or more terminals within an education resource system, each comprising distinct sharing capabilities. The terminals exchange information on various educational facets, encompassing variations and expenditures per share data, within the framework of a programming-type fuzzy objective function, constrained by the parameters of an educational information system. In these scenarios, the transfer of resources from one terminal to another is interlinked, introducing complexities that warrant a comprehensive examination. Notably, the consideration of greater downloading resources in specific cases is proposed for enhanced practicality. The primary objective of this article is to minimize network congestion within different educational networks, given fixed priority grades assigned to the terminals. To achieve this, the concept of a Lexicographic minimum solution is introduced to address max-min fuzzy relation inequalities, aligning with the defined objectives. The article presents a detailed and effective scenario for implementing the Lexicographic minimal solution. For validation purposes, the proposed scenario is supported by illustrative examples, offering tangible insights into its applicability and efficacy. |
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| AbstractList | This study delves into the application of min-max fuzzy relation systems, specifically focusing on equality and inequality, in the examination of educational institution networks and their resource-sharing dynamics, akin to a P2P network structure. Expanding upon this framework, this article intricately explores a mathematical system featuring three or more terminals within an education resource system, each comprising distinct sharing capabilities. The terminals exchange information on various educational facets, encompassing variations and expenditures per share data, within the framework of a programming-type fuzzy objective function, constrained by the parameters of an educational information system. In these scenarios, the transfer of resources from one terminal to another is interlinked, introducing complexities that warrant a comprehensive examination. Notably, the consideration of greater downloading resources in specific cases is proposed for enhanced practicality. The primary objective of this article is to minimize network congestion within different educational networks, given fixed priority grades assigned to the terminals. To achieve this, the concept of a Lexicographic minimum solution is introduced to address max-min fuzzy relation inequalities, aligning with the defined objectives. The article presents a detailed and effective scenario for implementing the Lexicographic minimal solution. For validation purposes, the proposed scenario is supported by illustrative examples, offering tangible insights into its applicability and efficacy. |
| Author | Zhang, Lei |
| Author_xml | – sequence: 1 givenname: Lei surname: Zhang fullname: Zhang, Lei organization: School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, People's Republic of China |
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| Cites_doi | 10.1016/j.dam.2006.08.011 10.1023/A:1022848114005 10.1016/j.mcm.2010.01.006 10.1016/j.cam.2023.115089 10.1007/s10700-008-9029-y 10.1109/FSKD.2012.6233956 10.1109/Access.6287639 10.1080/16168658.2020.1761511 10.1016/j.fss.2017.08.001 10.1109/ACCESS.2017.2731819 10.1504/IJBIC.2023.130549 10.1016/j.ins.2011.09.030 10.1007/978-94-017-1650-5 10.1016/j.fss.2019.02.016 10.1016/j.cie.2011.09.012 10.1007/s13042-016-0527-x 10.1016/j.ins.2005.11.008 10.1016/j.chaos.2023.113440 10.1016/j.ins.2015.07.015 10.1016/B978-1-4832-1450-4.50017-1 10.1109/ACCESS.2018.2877199 10.1109/TFUZZ.2017.2771406 10.31181/sa310823p 10.1016/S0019-9958(76)90446-0 10.1016/j.cie.2014.03.024 10.1016/j.laa.2019.12.017 10.1109/91.855920 10.1109/ACCESS.2018.2841989 10.1007/s10700-019-09306-8 10.1016/j.chaos.2006.07.051 10.1016/j.fss.2014.10.008 10.1007/s40815-018-0530-3 10.1109/TFUZZ.2015.2428716 10.1109/TFUZZ.91 10.1016/j.najef.2022.101672 10.1016/0022-247X(91)90222-L 10.1016/j.ins.2016.04.014 10.1007/s10700-019-09305-9 |
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| Title | Max-min fuzzy bi-level programming: resource sharing system with application |
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