## 3 Results and Discussion
### Anris  
The results of the best ANFIS structure for estimating the \(MR\) of parboiled hulls in different conditions are given in Table 3.  
In the present study, the findings of an experimental investigation and the modeling prediction using ANFIS were compared and employed to estimate the \(MR\) of parboiled hulls. Information on the most preside algorithms is shown in Table 3.  
In ANFIS analysis, as in other models used, the best architecture must be designed. To achieve this goal, different ANFIS models have been designed using a trial-and-error method to determine the number of fuzzy rules in output prediction. This model used eight types of membership functions: psigmf, dsigmf, pimf, Gasuss2 mf, \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline \multirow{2}{*}{**Network**} & **Training** & \multirow{2}{*}{**Activation**} & \multirow{2}{*}{**Number of Layers**} & \multirow{2}{*}{\(MSE\)} & \multicolumn{3}{c}{**Test**} & \multicolumn{3}{c}{**Train**} & \\  & & & & & & \(R^{2}\) & \(MAE\) & \(R^{2}\) & \(MAE\) & **Epoch** \\ \hline FFBP & LM & TAN-TAN-TAN & 3-8-8-1 & 0.0059 & 0.9991 & 0.0423 & 0.9967 & 0.0618 & 144 \\ FFBP & BR & PUR-TAN-TAN & 3-5-5-1 & 0.0073 & 0.9982 & 0.0501 & 0.9711 & 0.0924 & 118 \\ CFBP & LM & TAN-LOG-PUR & 3-10-8-1 & 0.0068 & 0.9989 & 0.0449 & 0.9968 & 0.0599 & 68 \\ CFBP & BR & TAN-TAN-TAN & 3-5-5-1 & 0.0080 & 0.9979 & 0.0533 & 0.9899 & 0.0855 & 132 \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Best selected topologies, including testing and training, different layers and neurons for FFBP, and CFBP for moisture ratio. \begin{table}
\begin{tabular}{c c} \hline \hline
**Result** & **ANFIS Modeling Results** \\ \hline Sugeno-type & Fuzzy structure \\ Genfis1 & Basic FIS for training \\
3-3-3 & Number of membership functions for each entry \\ Gaussian (gaussmf) & Type of membership function for each entry \\
1000 & Epoch \\ Linear & Type of membership function for each output \\ Hybrid & Training algorithm \\
3 & Number of entries \\
27 & Number of output membership functions \\
114 & Number of data for training \\
49 & Number of data to evaluate \\
27 & Number of fuzzy rules \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Information on the best model for the \(MR\) of parboiled hulls in ANFIS. trimf, and trapmf. As can be seen, the Gaussian membership function (gaussmf) is widely employed in ANFIS modeling using training and test data as a membership function. It was found that this membership function due to the lower values of \(MSE\) and higher \(R^{2}\) and 27 fuzzy rules with structure (\(3\times 3\times 3\)) showed the best performance and estimation compared to all membership functions to predict the \(MR\) of parboiled hulls in infrared-hot air drying (Table 3). The number of functional membership rules was three to five. This membership function is the most applied in ANFIS networks. Indeed, it is actually suitable in terms of values and relation to the types of membership functions. Finally, the three fuzzy rules for each input exceed the number of other membership rules. Thus, 27 fuzzy rules (\(3\times 3\times 3\)) revealed the highest efficiency for predicting the \(MR\) of parboiled hulls in an IR-HA drying (Table 3). The findings obtained for ANFIS modeling are tabulated in Table 4. It should be noted that the accuracy of the ANFIS model could be improved by increasing the number of membership functions; however, it drastically increases the number of rules. As observed, the lowest \(MSE\) and the highest \(R^{2}\) were provided by the ANFIS algorithm. In fact, the model potentially predicted the \(MR\) with a coefficient of determination of 0.995 and the \(MSE\) of 0.0036. In a study conducted by [PERSON] et al. (2019) who used a similar technique to estimate the \(MR\) of quintee using IR drying, they claimed the values of 0.9999 and 0.0041 for \(R^{2}\) and \(RMSE\), respectively. In another research, [PERSON] et al. (2019) used the ANFIS model to predict the green peas moisture ratio (\(MR\)) by using a hot air-rotary drum dryer.