## 4 Experiment and Analysis
### Experimental Method and Analysis of Results  
The predicted performance of grid-based AFNIS and FCM clustering-based ANFIS, which are general rule generation methods, and of the increasing tree structure based on the CFCM clustering method proposed in this study were compared and analyzed. As described above, a grid-based ANFIS creates rules by dividing the input space into lattices, and FCM clustering-based ANFIS clusters the input space using FCM clustering to create rules. The proposed method uses CFCM clustering in input and output spaces to create contexts and clusters to create rules. First, the grid-based ANFIS experiment confirmed the predicted performance by increasing the MF by 1 from 2 to 5. By adjusting the number of clusters and the fuzzification coefficient, the FCM-clustering-based ANFIS experiment was carried out. The number of clusters increased by 2 from 2 to 20 and the coefficient of fuzzification was set at 2 to confirm the performance anticipated. Finally, for the experiment on AFNIS using the incremental tree structure based on the CFCM clustering method, which is the method proposed in this study, we designed three CFCM-clustering-based ANFISs with two inputs and one output as an incremental tree structure. The entire input variable was then ranked according to the correlation coefficient and used as input to each ANFIS. In the CFCM clustering method, the number of contexts (\(p\)) increased by 2 from 2 to 6, and the number of clusters (\(c\)) increased by 2 from 2 to 20, confirming the predicted performance. Each ANFIS was performed 10 iterations, and the value with the minimum verification root mean square error (RMSE) was used as the result value. All experiments for Grid-ANFIS, FCM-ANFIS, Incremental-CFCM-ANFIS, LR and RBFN were conducted using Matlab, and the OS is a window10 environment. Table 1 summarizes the prediction performance of the grid-based ANFIS, and Figure 6 shows the prediction results of the grid-based ANFIS. As can be seen in Table 1, when there are two MFs, 256 rules are created, and the verification root mean square error (RMSE) is \(\sim\)2.2471. When there are three, four, or five MFs, the number of rules increases exponentially, indicating a calculation error. Table 2 summarizes the prediction performance of ANFIS based on FCM clustering, and Figure 7 shows the prediction results. As can be seen in Table 2, when there are 10 clusters, 10 rules are created and the verification RMSE is \(\sim\)2.0671. The prediction efficiency of the CFCM-based ANFIS in the form of an incremental tree is summarized in Table 3, which is the approach suggested in this report. Figure 8 shows the prediction results. As can be seen in Table 3, when there are 6 contexts and 20 clusters, 120 rules are created and the verification RMSE is \(\sim\)1.8705, yielding the best prediction performance. Table 4 compares and analyzes the prediction performance of grid-ANFIS, FCM-ANFIS and Incremental-CFCM-ANFIS, and the linear regression (LR) model and the radial basis function network (RBFN) model used for prediction problems. For LR and RBFN, the verification RMSE values were approximately 3.04 and 25.45 respectively, and a fuzzy rule was not generated. In Grid-ANFIS, if there are 2 membership functions, 256 rules are created and the verification RMSE value is about 2.25. In FCM-ANFIS, when the number of clusters is 10, 10 rules are created and the verification RMSE value is about 2.07. Finally, the proposed method shows that when the number of contexts is 6 and the number of clusters is 20, 120 rules are generated and the verification RMSE value is about 1.87, showing the best prediction performance. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Number of MFs** & **Number of Rules** & **Training RMSE** & **Testing RMSE** \\ \hline \multirow{4}{*}{Grid-ANFIS} & 2 & 256 & 0.6728 & 2.2471 \\  & 3 & - & - & - \\  & 4 & - & - & - \\  & 5 & - & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Prediction experiment results from grid-based ANFIS.