Weighted minimax programming subject to the max-min fuzzy relation inequalities

Miaoxia Chen; Abdul Samad Shibghatullah; Kasthuri Subramaniam; Xiaopeng Yang; Miaoxia Chen; Abdul Samad Shibghatullah; Kasthuri Subramaniam; Xiaopeng Yang

doi:10.3934/math.2024665

AIMS Mathematics

2024, Volume 9, Issue 6: 13624-13641. doi: 10.3934/math.2024665

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Research article

Weighted minimax programming subject to the max-min fuzzy relation inequalities

1.
Institute of Computer Science & Digital Innovation, UCSI University, Kuala Lumpur, 56000, Malaysia
2.
Department of Education, Hanshan Normal University, Chaozhou, 521041, China
3.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China

Received: 31 December 2023 Revised: 06 February 2024 Accepted: 18 March 2024 Published: 12 April 2024
MSC : 90C70, 90C90

Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.
- fuzzy relation inequality,
- max-min composition,
- P2P network system,
- weighted minimax programming,
- mathematical model
Citation: Miaoxia Chen, Abdul Samad Shibghatullah, Kasthuri Subramaniam, Xiaopeng Yang. Weighted minimax programming subject to the max-min fuzzy relation inequalities[J]. AIMS Mathematics, 2024, 9(6): 13624-13641. doi: 10.3934/math.2024665

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Abstract

Recently, max-min fuzzy relation inequalities (FRIs) have been used to model a (peer-to-peer) P2P network system. Any feasible scheme in the P2P network system is reflected by a solution of the max-min FRIs. One of the objectives of system managers is to decrease network congestion. To satisfy this objective, we attempt to minimize a weighted minimax function motivated by existing research. As a consequence, we establish a weighted minimax programming model in which the constraint is the max-min FRIs. Our goal in this work is to develop an effective algorithm to obtain the optimal solution of the optimization model. The so-called SCP-based algorithm is proposed to find the optimal solution. A numerical example shows the efficiency of our proposed SCP-based algorithm.

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