Finding minimal solutions to the system of addition-min fuzzy relational inequalities

In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not u...

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Bibliographic Details
Published in:Fuzzy optimization and decision making 2022-12, Vol.21 (4), p.581-603
Main Authors: Wu, Yan-Kuen, Wen, Ching-Feng, Hsu, Yuan-Teng, Wang, Ming-Xian
Format: Article
Language:English
Subjects:
Algorithms
Artificial Intelligence
Calculus of Variations and Optimal Control
Optimization
File sharing
Inequalities
Iterative algorithms
Iterative methods
Mathematical Logic and Foundations
Mathematics
Mathematics and Statistics
Operations Research/Decision Theory
Optimization
Peer to peer computing
Probability Theory and Stochastic Processes
Variables
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Summary:In the literature, a BitTorrent-like peer-to-peer file-sharing system has been modelled as a system of addition-min fuzzy relational inequalities (FRIs). Finding all minimal solutions of such a system is considered a difficult task because the minimal solutions to addition-min FRIs are usually not unique and are often infinite in number. In this paper, we study the properties of the minimal solutions of such a system and propose an iterative algorithm to find the minimal solutions for any given solution (included the maximum solution). The proposed algorithm not only finds the minimal solutions efficiently, but also finds many minimal solutions in different iterative sequences of variables.
ISSN:1568-4539
1573-2908
DOI:10.1007/s10700-021-09377-6