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Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities

Author

Listed:
  • Jianjun Qiu

    (Lingnan Normal University)

  • Xiaopeng Yang

    (Hanshan Normal University)

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.

Suggested Citation

  • Jianjun Qiu & Xiaopeng Yang, 2022. "Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities," Fuzzy Optimization and Decision Making, Springer, vol. 21(2), pages 291-317, June.
    • Handle: RePEc:spr:fuzodm:v:21:y:2022:i:2:d:10.1007_s10700-021-09368-7
    DOI: 10.1007/s10700-021-09368-7
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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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