Fuzzy relation lexicographic programming for modelling P2P file sharing system
Considering the requirement of the biggest download speed, a Peer-to-Peer (P2P) file sharing system can be reduced into a system of max–min fuzzy relation inequalities. In order to decrease the network congestion under some fixed priority grade of the terminals, fuzzy relation lexicographic programming is proposed to model the P2P file sharing system. For solving the proposed problem, we define concept of feasible index set and discuss some simple properties. Based on the feasible index set, a novel algorithm is developed to find the optimal solution with an illustrative example.
KeywordsFuzzy relation inequality Lexicographic order Max–min composition Fuzzy relation equation Peer-to-Peer network system System optimization
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All the authors declare that they have no conflict of interest.
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This article does not contain any studies with human participants or animals performed by any of the authors.
- Li J-X, Yang S-J (2012) Fuzzy relation inequalities about the data transmission mechanism in bittorrent-like peer-to-peer file sharing systems. In: Proceedings of the 2012 9th international conference on fuzzy systems and knowledge discovery, FSKD, pp 452–456Google Scholar
- Sanchez E (1977) Solutions in composite fuzzy relation equations: application to medical diagnosis in Brouwerian logic. In: Gupta MM, Saridis GN, Gaines BR (eds) Fuzzy automata and decision processes. North-Holland, Amsterdam, pp 221–234Google Scholar
- Yang J-H, Cao B-Y (2005) Geometric programming with fuzzy relation equation constraints. In: Proceedings of IEEE international conference on fuzzy systems, pp 557–560Google Scholar