# Fuzzy relation lexicographic programming for modelling P2P file sharing system

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## Abstract

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.

## Keywords

Fuzzy relation inequality Lexicographic order Max–min composition Fuzzy relation equation Peer-to-Peer network system System optimization## Notes

### Compliance with ethical standards

#### Conflict of interest

All the authors declare that they have no conflict of interest.

#### Human and animal rights

This article does not contain any studies with human participants or animals performed by any of the authors.

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