# Performance Comparison of ANFIS Models by Input Space Partitioning Methods
## 4 Experimental Method and Result Analysis
### Combined Cycle Power Plant Database  
Table 1 lists the results for the ANFIS1 model using CCPP data. The two inputs of AT and RH were used when two input variables were used, and AT, V, and AP were used when three input variables were used. When three input variables were used and MF was set to 5, the model showed the best performance. Table 2 lists the results for the ANFIS2 model. The ANFIS2 model using the SC method showed the best performance when the radius of the cluster was set to 0.3.  
Figure 9: Input variable recombination method.  
Figure 10 shows the RMSE values of the ANFIS1 model using the test data, and Figure 11 shows the RMSE values of the ANFIS2 model using the test data.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Radii** & **Number of Rules** & **Training RMSE** & **Testing RMSE** \\ \hline \multirow{8}{*}{ANFIS2} & 0.2 & 42 & 3.80 & 4.18 \\  & 0.3 & 17 & 3.99 & 4.13 \\  & 0.4 & 7 & 4.07 & 4.22 \\  & 0.5 & 5 & 4.09 & 4.26 \\  & 0.6 & 2 & 4.24 & 4.26 \\  & 0.7 & 2 & 4.13 & 4.35 \\  & 0.8 & 3 & 4.14 & 4.22 \\  & 0.9 & 2 & 4.20 & 4.26 \\ \hline \hline \end{tabular}
\end{table}
Table 2: Experimental results of ANFIS2 model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Algorithm** & **Input** & **Membership** & **Number of Rules** & **Training RMSE** & **Testing RMSE** \\ \hline \multirow{8}{*}{ANFIS1} & 2 Inputs & 3 & 9 & 4.43 \\  & (AT, RH) & 4 & 16 & 4.45 & 4.52 \\  & 5 & 25 & 4.40 & 4.60 \\ \cline{1-1} \cline{2-5}  & & 2 & 8 & 4.27 & 4.35 \\ \cline{1-1}  & 3 Inputs & 3 & 27 & 4.04 & 4.24 \\ \cline{1-1}  & (AT, V, AP) & 4 & 64 & 3.90 & 4.21 \\ \cline{1-1}  & 5 & 125 & 3.92 & 4.13 \\ \cline{1-1} \cline{2-5}  & & 2 & 16 & 4.02 & 4.17 \\ \cline{1-1}  & 3 & 81 & 3.84 & 4.21 \\ \cline{1-1}  & 4 & 256 & 3.49 & 4.45 \\ \cline{1-1}  & 5 & 625 & 3.22 & 5.19 \\ \hline \hline \end{tabular}
\end{table}
Table 1: Experimental results of ANFIS1 model. RMSE (root-mean square error), AT (time-averaged ambient temperature), AP (ambient pressure), RH (relative humidity), and V (exhaust vacuum), ANFIS (adaptive neuro-fuzzy inference system).  
Figure 10: The RMSE value obtained from ANFIS1 using test data.  
Table 3 lists the results for the ANFIS3 model. The ANFIS3 model using the FCM clustering method showed the best performance when the number of clusters was set to 30. Table 4 lists the results for the ANFIS4 model. The ANFIS4 model performed two experiments with fixed contexts of 6 and 10. Among them, when the context was fixed to 10 and the number of clusters was set to 17, the best performance was shown. Figures 12 and 13 show the RMSE values of the ANFIS3 and ANFIS4 models using the test data.  
Table 5 summarizes the prediction performance of each ANFIS model. When the context of the ANFIS4 model was fixed to 10 and the number of clusters was set to 17, 170 rules were generated and the testing RMSE value was 3.99. Figure 14 shows the best prediction performance for each ANFIS model. In Figure 14, the \(x\)-axis represents the respective ANFIS models, where 1 represents the ANFIS1 model, 2 represents the ANFIS2 model, 3 represents the ANFIS3 model, and 4 represents the ANFIS4 model.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & **Context (p) \& Cluster (c)** & **Number of** & **Training** & **Testing** \\ \cline{2-5}  & **p** & **c** & **Rules** & **RMSE** & **RMSE** \\ \hline \multirow{8}{*}{6} & 2 & 12 & 4.11 & 4.15 \\  & 3 & 18 & 4.11 & 4.14 \\  & 4 & 24 & 4.04 & 4.20 \\  & 5 & 30 & 4.11 & 4.13 \\  &  
Figure 14: The RMSE values obtained from ANFIS1, 2, 3, and 4 using testing data.  
Figure 12: The RMSEs value obtained from ANFIS3 using test data.  
Figure 13: RMSE values obtained from ANFIS4 using test data.