@article{Zhu2024, 
author = {Guocheng Zhu and Zhining Wang and Xiaopeng Yang},
title = {On the minimal solution for max-product fuzzy relation inequalities},
year = {2024},
journal = {AIMS Mathematics},
volume = {9},
number = {11},
pages = {30667-30685},
keywords = {fuzzy relation inequalities, max-product composition, minimal solution},
url = {https://www.sciopen.com/article/10.3934/math.20241481},
doi = {10.3934/math.20241481},
abstract = {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.}
}