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Finding minimal solutions to the system of addition-min fuzzy relational inequalities

Author

Listed:
  • Yan-Kuen Wu

    (Zhejiang Yuexiu University of Foreign Languages)

  • Ching-Feng Wen

    (Kaohsiung Medical University
    Kaohsiung Medical University Hospital)

  • Yuan-Teng Hsu

    (Shanghai Business School)

  • Ming-Xian Wang

    (Zhejiang Yuexiu University of Foreign Languages)

Abstract

In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables.

Suggested Citation

  • Yan-Kuen Wu & Ching-Feng Wen & Yuan-Teng Hsu & Ming-Xian Wang, 2022. "Finding minimal solutions to the system of addition-min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 21(4), pages 581-603, December.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:4:d:10.1007_s10700-021-09377-6
    DOI: 10.1007/s10700-021-09377-6
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    References listed on IDEAS

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    1. Ya-Ling Chiu & Sy-Ming Guu & Jiajun Yu & Yan-Kuen Wu, 2019. "A single-variable method for solving min–max programming problem with addition-min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 433-449, December.
    2. Sy-Ming Guu & Yan-Kuen Wu, 2019. "Multiple objective optimization for systems with addition–min fuzzy relational inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 18(4), pages 529-544, December.
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