Lexicographic Minimum Solution to the System of Fuzzy Relation Inequalities With Addition-Min-Product Composition

The addition-min-product fuzzy relation inequalities were recently introduced to model peer-to-peer file-sharing systems, considering scenarios where the terminals transmit their local file data at varying quality levels. Previous research primarily focused on min-max fuzzy relation programming, whi...

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Bibliographic Details
Published inIEEE transactions on fuzzy systems Vol. 33; no. 3; pp. 1088 - 1098
Main Authors Shu, Qianyu, Zhu, Guocheng, Wang, Xingming, Yang, Xiaopeng
Format Journal Article
LanguageEnglish
Published IEEE 01.03.2025
Subjects
Addition-min-product composition
fuzzy relation inequality (FRI)
Fuzzy systems
Indexes
lexicographic minimum solution
Linear programming
Minimax techniques
Network systems
Optimization
peer-to-peer (P2P) network system
Peer-to-peer computing
Programming
Smoothing methods
Vectors
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ISSN1063-6706
1941-0034
DOI10.1109/TFUZZ.2024.3514746

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Summary:The addition-min-product fuzzy relation inequalities were recently introduced to model peer-to-peer file-sharing systems, considering scenarios where the terminals transmit their local file data at varying quality levels. Previous research primarily focused on min-max fuzzy relation programming, which assumed equal treatment for all terminals. However, this approach is inadequate when the terminals need to be differentiated or assigned fixed priority grades. To address network congestion while considering terminal priority, this study explores the lexicographic minimum solution for the addition-min-product FRIs. We propose a detailed algorithm to compute the lexicographic minimum solution, associated with a numerical illustrative example.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2024.3514746