Approximation of fuzzy numbers by truncated and non-truncated operators of max-product kind

In this study, we extended truncated and non-truncated max-product type operators to any compact interval. In this extension, we examined their approximation rates and approximation properties. Additionally, we demonstrated that these operators preserve monotonicity and shape properties within compact intervals. To address practical applications, we generated fuzzy numbers while preserving the support and core of the approximated fuzzy number in a specific manner. Subsequently, we utilized these fuzzy numbers to improve approximation estimates using metrics such as $D_{C},\tilde{D}_{C},$ and $L^{1}-$type. As a result, we effectively applied these techniques to interpret medical data, providing a method for accurately predicting the survival rates of cancer patients and foreseeing potential developments with precision. Finally, we provided a comprehensive evaluation with comparative data, illustrative graphs, and tables. These sources show that these operators facilitate the approximation of fuzzy functions and have the potential to support medical research and statistical analysis.