Addition-min fuzzy relation inequalities with application in BitTorrent-like peer-to-peer file sharing system.

*(English)*Zbl 1397.90433Summary: The data transmission mechanism in BitTorrent-like Peer-to-Peer (P2P) file sharing systems may be reduced to some addition-min fuzzy relation inequalities. The solution set of addition-min fuzzy relation inequalities plays an important role in the corresponding optimization problem. In this paper, we study some properties of the solutions to such a system. Convexity of the solution set and number of minimal solutions are discussed, with comparison to those of the classical max-\(T\) fuzzy relation equations or inequalities. Besides, vertex solution and variable-ordering minimal solution are also investigated, with application in BitTorrent-like P2P file sharing system. Two numerical examples are given to illustrate the feasibility and efficiency of the algorithm for solving the variable-ordering solution.

##### MSC:

90C70 | Fuzzy and other nonstochastic uncertainty mathematical programming |

90C90 | Applications of mathematical programming |

68M11 | Internet topics |

##### Keywords:

fuzzy relation inequalities; addition-min composition; fuzzy relation equation; minimal solution; convex set; BitTorrent-like P2P file sharing systems
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\textit{X.-P. Yang} et al., Fuzzy Sets Syst. 343, 126--140 (2018; Zbl 1397.90433)

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##### References:

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