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AIMS Mathematics

2024, Volume 9, Issue 11: 30667-30685. doi: 10.3934/math.20241481
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Research article

On the minimal solution for max-product fuzzy relation inequalities

  • 1.
    School of Humanities Education, Guangdong Innovative Technical College, Dongguan, 523960, China
  • 2.
    School of Mathematics and Statistics, Hanshan Normal University, Chaozhou, 521041, China
  • Received: 13 July 2024 Revised: 17 October 2024 Accepted: 23 October 2024 Published: 28 October 2024

  • MSC : 90C70, 90C90

  • Minimal solutions play a crucial role in constructing the complete solution set of the max-product fuzzy relation inequalities, as well as in solving the corresponding fuzzy relation optimization problems. In this work, we propose a sufficient and necessary condition for checking whether a given solution is minimal in the max-product system. Our proposed approach is useful for eliminating non-minimal solutions from the set of all quasi-minimal solutions. Our proposed checking approach helps reduce computational complexity when solving the max-product system or related optimization problems.

    Citation: Guocheng Zhu, Zhining Wang, Xiaopeng Yang. On the minimal solution for max-product fuzzy relation inequalities[J]. AIMS Mathematics, 2024, 9(11): 30667-30685. doi: 10.3934/math.20241481

    Related Papers:

  • Minimal solutions play a crucial role in constructing the complete solution set of the max-product fuzzy relation inequalities, as well as in solving the corresponding fuzzy relation optimization problems. In this work, we propose a sufficient and necessary condition for checking whether a given solution is minimal in the max-product system. Our proposed approach is useful for eliminating non-minimal solutions from the set of all quasi-minimal solutions. Our proposed checking approach helps reduce computational complexity when solving the max-product system or related optimization problems.



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