Centralized solution in max-min fuzzy relation inequalities

Miaoxia Chen; Guocheng Zhu; Shayla Islam; Xiaopeng Yang; Miaoxia Chen; Guocheng Zhu; Shayla Islam; Xiaopeng Yang

doi:10.3934/math.2025361

AIMS Mathematics

2025, Volume 10, Issue 4: 7864-7890. doi: 10.3934/math.2025361

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Centralized solution in max-min fuzzy relation inequalities

1.
Department of Education, Hanshan Normal University, Chaozhou, 521041, China
2.
Institute of Computer Science & Digital Innovation, UCSI University, Kuala Lumpur, 56000, Malaysia
3.
School of Humanities Education, Guangdong Innovative Technical College, Dongguan, 523960, China
4.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China

Received: 21 January 2025 Revised: 17 March 2025 Accepted: 19 March 2025 Published: 03 April 2025
MSC : 90C70, 90C90

In recent years, the peer-to-peer (P2P) educational information sharing system was modeled by a system of fuzzy relation inequalities (FRIs) with addition-min or max-min composition. The max-min FRIs system was applicable to the P2P network considering the highest download traffic among the terminals. Moreover, every solution to such a max-min FRIs system corresponds exactly to one feasible flow control scheme. To embody the stability of a given feasible scheme, we introduce the concept of the widest symmetrical interval solution (WSIS), regarding the corresponding solution in the max-min FRIs system. Some effective procedures are proposed to find the WSIS regarding a provided solution. In addition, aiming to find the most stable feasible scheme, we further define the concept of a centralized solution. Some effective procedures are also proposed to find the centralized solution regarding the max-min FRIs system. Some numerical examples are provided, respectively, to demonstrate our proposed resolution procedures. Our obtained centralized solution will provide decision support for system administrators considering the stability of the feasible scheme.
- max-min composition operation,
- P2P network system,
- fuzzy relation inequality,
- widest symmetrical interval solution,
- centralized solution
Citation: Miaoxia Chen, Guocheng Zhu, Shayla Islam, Xiaopeng Yang. Centralized solution in max-min fuzzy relation inequalities[J]. AIMS Mathematics, 2025, 10(4): 7864-7890. doi: 10.3934/math.2025361

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Abstract

In recent years, the peer-to-peer (P2P) educational information sharing system was modeled by a system of fuzzy relation inequalities (FRIs) with addition-min or max-min composition. The max-min FRIs system was applicable to the P2P network considering the highest download traffic among the terminals. Moreover, every solution to such a max-min FRIs system corresponds exactly to one feasible flow control scheme. To embody the stability of a given feasible scheme, we introduce the concept of the widest symmetrical interval solution (WSIS), regarding the corresponding solution in the max-min FRIs system. Some effective procedures are proposed to find the WSIS regarding a provided solution. In addition, aiming to find the most stable feasible scheme, we further define the concept of a centralized solution. Some effective procedures are also proposed to find the centralized solution regarding the max-min FRIs system. Some numerical examples are provided, respectively, to demonstrate our proposed resolution procedures. Our obtained centralized solution will provide decision support for system administrators considering the stability of the feasible scheme.

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