Maximum amplitude interval solution of a given solution in min-product system

Xiaobin Yang; Guocheng Zhu; Xiaopeng Yang; Xiaobin Yang; Guocheng Zhu; Xiaopeng Yang

doi:10.3934/math.20251150

AIMS Mathematics

2025, Volume 10, Issue 11: 26132-26152. doi: 10.3934/math.20251150

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Research article

Maximum amplitude interval solution of a given solution in min-product system

1.
Asset Management Department, Hanshan Normal University, Chaozhou 521041, China
2.
School of Humanities Education, Guangdong Innovative Technical College, Dongguan 523960, China
3.
School of Mathematics and Statistics, Hanshan Normal University, Chaozhou 521041, China

Received: 30 July 2025 Revised: 02 October 2025 Accepted: 23 October 2025 Published: 12 November 2025
MSC : 90C70, 90C90

In a supply chain system, the price of the goods should satisfy some requirements of the consumer. These requirements have been exactly characterized by a group of min-product fuzzy relation inequalities (FRIs). Correspondingly, any feasible pricing scheme is characterized by a solution of the min-product FRIs system. For a given pricing scheme, or say a given solution in the min-product FRIs, the flexibility is reflected by the maximum amplitude, or equivalently the maximum amplitude interval solution (MAIS). Motivated by such an application background, this work attempts to study the MAIS in min-product FRIs. An efficient algorithm is discovered for computing the MAIS of a solution within the given min-product system. The MAIS will help the system manager be aware of the flexibility of a given pricing scheme and produce better decision-making.
- min-product composition,
- fuzzy relation inequality,
- pricing scheme,
- supply chain,
- stability
Citation: Xiaobin Yang, Guocheng Zhu, Xiaopeng Yang. Maximum amplitude interval solution of a given solution in min-product system[J]. AIMS Mathematics, 2025, 10(11): 26132-26152. doi: 10.3934/math.20251150

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Abstract

In a supply chain system, the price of the goods should satisfy some requirements of the consumer. These requirements have been exactly characterized by a group of min-product fuzzy relation inequalities (FRIs). Correspondingly, any feasible pricing scheme is characterized by a solution of the min-product FRIs system. For a given pricing scheme, or say a given solution in the min-product FRIs, the flexibility is reflected by the maximum amplitude, or equivalently the maximum amplitude interval solution (MAIS). Motivated by such an application background, this work attempts to study the MAIS in min-product FRIs. An efficient algorithm is discovered for computing the MAIS of a solution within the given min-product system. The MAIS will help the system manager be aware of the flexibility of a given pricing scheme and produce better decision-making.

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