## 3 Results and Discussion
### ANFIS Model  
The experimental data of the treatment and control groups were randomly divided into three sets for the training (60%), validation (18%), and testing (22%) the ANFIS model. Each input/output pair consisted of two inputs (storage temperature and storage days) and one output (_Salmonella_ population). During the training phase, initial ANFIS models were generated using the grid partition method, and eight different types of input membership functions were tested. The final ANFIS architecture had two membership functions for each input variable and a linear membership function for the output variable, and eight if-then rules were constructed for high-quality prediction. The correlation between experimental and predicted _Salmonella_ populations with different membership functions at the training and prediction phases is shown in Figure S2. For ANFIS models with most membership functions, except for trapmf, the data points show a linear distribution in the training and prediction stages, and the regression lines in the training and prediction stages are highly coincident. The RMSE, RPD, and R2 for the experimental and predicted data during the training and prediction phases are shown in Table 1. It shows that the performance of the ANFIS model was influenced by the type of MFs used. Based on the standard that the RMSE should be minimized and the RPD should be greater than 3, the ANFIS model with the \"gaussmf\" MF showed better performance during both the training and prediction phases compared to other MFs. To visually demonstrate whether the predicted values of each model aligned with the experimental data and general knowledge, the predicted _Salmonella_ populations of the ANFIS models with different MFs were depicted as colored surfaces, as shown in Figure S3. It showed that the model with gaussmf produced the smoothest output surface without unnecessary fluctuations, and the curve shape at different temperatures corresponded well with both the experimental data and general knowledge. Therefore, we proposed using the ANFIS model with gaussmf to predict _Salmonella_ populations in fresh-cut wax gourd during storage. Both the populations of _Salmonella_ observed in the experiments and the populations of _Salmonella_ predicted by ANFIS with gaussmf are depicted in Figure 4.  
Mathematical models for describing microbe growth, such as the Gompertz model [46], Baranyi model [47], and Huang's model [48], have inherent limitations. Usually, these formulas are proposed to describe usual growth curves rather than constant lines or declined curves. Additionally, the best fitting curves for these formulas are sigmoid-shaped curves, which should consist of the lag, exponential, and stationary phases. Although mathematical models are very suitable for describing growth kinetics and have the advantage of providing the physical or biological meanings of some functions, its application in predicting the complex and variable population curves of microbes may be limited. The ANFIS model is established upon fuzzy inference and learns by an artificial neural \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Membership**} & \multicolumn{3}{c}{**Training**} & \multicolumn{3}{c}{**Prediction**} \\ \cline{2-7}  & **RMSE** & **RPD** & **R2** & **RMSE** & **RPD** & **R2** \\ \hline trimf & 0.118636 & 11.8055 & 0.988 & 0.204105 & 6.2084 & 0.985 \\ trapmf & 0.152206 & 9.2017 & 0.9952 & 0.369718 & 3.4274 & 0.9811 \\ gbellmf & 0.132012 & 10.6093 & 0.995 & 0.126194 & 10.0414 & 0.9895 \\ gaussmf & 0.12133 & 11.5433 & 0.9933 & 0.116264 & 10.8990 & 0.9921 \\ gauss2 mf & 0.109365 & 12.8062 & 0.9952 & 0.119431 & 10.6100 & 0.9828 \\ pimf & 0.181447 & 7.7188 & 0.9943 & 0.168392 & 7.5251 & 0.9789 \\ dsigmf & 0.186646 & 7.5038 & 0.9957 & 0.141256 & 8.9707 & 0.9861 \\ psigmf & 0.186646 & 7.5038 & 0.9957 & 0.141256 & 8.9707 & 0.9861 \\ \hline \hline \end{tabular}
\end{table}