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Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities

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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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Authors and Affiliations

  1. School of International Business, Shaoxing Key Laboratory of Intelligent Monitoring and Prevention of Smart City, Zhejiang Yuexiu University of Foreign Languages, Shaoxing City, Zhejiang, China

    Yan-Kuen Wu

  2. Center for Fundamental Science and Research Center for Nonlinear Analysis and Optimization, Kaohsiung Medical University, Kaohsiung, Taiwan

    Ching-Feng Wen

  3. Department of Medical Research, Kaohsiung Medical University Hospital, Kaohsiung, 80708, Taiwan, ROC

    Ching-Feng Wen

  4. Research Center of Finance, Shanghai Business School, Shanghai, China

    Yuan-Teng Hsu

  5. School of International Business, Zhejiang Yuexiu University of Foreign Languages, Shaoxing, 312000, Zhejiang, China

    Ming-Xian Wang

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  1. Yan-Kuen Wu
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  2. Ching-Feng Wen
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  3. Yuan-Teng Hsu
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  4. Ming-Xian Wang
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Correspondence to Yan-Kuen Wu or Ching-Feng Wen.

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Wu, YK., Wen, CF., Hsu, YT. et al. Some results for the minimal optimal solution of min-max programming problem with addition-min fuzzy relational inequalities. Fuzzy Optim Decis Making 21, 429–454 (2022). https://doi.org/10.1007/s10700-021-09371-y

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