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
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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