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

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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Acknowledgements

This work was partly supported by the National Natural Science Foundation of China (61877014), the NSF of Lingnan Normal University (ZL1811) and funds provided by Guangdong Province (2019KZDXM013, 2021A1515011091, 2020ZDZX3056, ZD201802, 2018A0303070009).

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Correspondence to Xiaopeng Yang.

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Qiu, J., Yang, . Min–max programming problem with constraints of addition-min-product fuzzy relation inequalities. Fuzzy Optim Decis Making 21, 291–317 (2022). https://doi.org/10.1007/s10700-021-09368-7

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  • DOI: https://doi.org/10.1007/s10700-021-09368-7

Keywords

  • Fuzzy relation inequality
  • Fuzzy relation equation
  • Addition-min-product composition
  • Min–max programming problem
  • Peer-to-Peer file sharing system