# Performance Comparison of ANFIS Models by Input Space Partitioning Methods
## 4 Experimental Method and Result Analysis
### Auto-MPG Database  
Table 6 lists the results for the ANFIS1 model using Auto-MPG data. We used the displacement and acceleration force when two input variables were used, and the displacement, weight, and acceleration force when three input variables were used. When four input variables were used, the displacement, horsepower, weight, and acceleration were used. When three input variables were used and MF was set to 2, the model showed the best performance. Figure 15 shows the RMSE values of the ANFIS1 model using the test data. The results of the ANFIS2 model are listed in Table 7. The ANFIS2 model using the SC method showed the best performance when the radius of the cluster was set to 0.8. Figure 16 shows the RMSE values of the ANFIS2 model using the test data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & **Input** & **Membership** & **Number of** & **Training** & **Testing RMSE** \\  & **Combination** & **Functions** & **Rules** & **RMSE** & **Testing RMSE** \\ \hline \multirow{8}{*}{ANFIS1} & 2 Inputs & 2 & 4 & 3.35 & 3.33 \\  & (displacement, & 3 & 9 & 3.24 & 3.47 \\  & acceleration) & 4 & 16 & 3.16 & 3.93 \\  & 5 & 25 & 2.78 & 5.07 \\ \cline{2-6}  & 3 Inputs & 2 & 8 & 2.69 & 3.28 \\ \cline{2-6}  & (displacement, & 3 & 27 & 2.29 & 7.01 \\ \cline{2-6}  & weight, & 4 & 64 & 1.84 & 11.14 \\ \cline{2-6}  & acceleration) & 5 & 125 & 0.98 & 19.90 \\ \cline{2-6}  & 4 Inputs & 2 & 16 & 2.04 & 3.37 \\ \cline{2-6}  & (displacement, & 3 & 81 & 1.25 & 10.34 \\ \cline{2-6}  & horsepower, & 4 & 256 & 0.11 & 19.69 \\ \cline{2-6}  & weight, & 5 & 625 & 0.01 & 12.44 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Experimental results of ANFIS1 model.  
Figure 15: The RMSE values obtained from ANFIS1 using testing data.  
The results for the ANFIS3 model are listed in Table 8. The ANFIS3 model using the FCM clustering method showed the best performance when the number of clusters was set to 5. The results for the ANFIS4 model are listed in Table 9. The ANFIS4 model performed two experiments with fixed contexts of 6 and 10. Among them, when the context was fixed to 6 and the number of clusters was set to 4, the best performance was shown. Figures 17 and 18 show the RMSE values of the ANFIS3 and ANFIS4 models using the test data.  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline \multirow{2}{*}{**Algorithm**} & \multicolumn{2}{c}{**Context (p) \& Cluster (c)**} & \multicolumn{1}{c}{**Number of**} & \multicolumn{1}{c}{**Training**} & \multicolumn{1}{c}{**Testing**} \\ \cline{2-5}  & **p** & **c** & **Rules** & **RMSE** & **RMSE** \\ \hline \multirow{9}{*}{**RMSE**} & \multirow{9}{*}{**10**} & 2 & 12 & 2.51 & 2.62 \\  & & 3 & 18 & 2.54 & 2.60 \\  & & 4 & 24 & 2.54 & 2.60 \\  & & 5 & 30 & 2.55 & 2.61 \\  & & 6 & 36 & 2.57 & 2.60 \\  & & 7 & 42 & 2.58 & 2.61 \\  & & 8 & 48 & 2.58 & 2.60 \\  & & 9 & 54 & 2.59 & 2.61 \\  & & 10 & 60 & 2.60 & 2.61 \\
6 & 11 & 66 & 2.61 & 2.61 \\  & & 12 & 72 & 2.61 & 2.62 \\  & & 13 & 78 & 2.61 & 2.62 \\  & & 14 & 84 & 2.62 & 2.62 \\  & & 15 & 90 & 2.63 & 2.62 \\  & & 16 & 96 & 2.63 & 2.62 \\  & & 17 & 112 & 2.63 & 2.63 \\  & & 18 & 118 & 2.63 & 2.63 \\  & & 19 & 124 & 2.64 & 2.63 \\  & & 20 & 130 & 2.64 & 2.64 \\ \hline \multirow{9}{*}{ANFIS4} & \multirow{9}{*}{**10**} & 2 & 20 & 2.53 & 2.62 \\  & & 3 & 30 & 5.55 & 2.61 \\  & & 4 & 40 & 2.57 & 2.61 \\  & & 5 & 50 & 2.57 & 2.61 \\  & & 6 & 60 & 2.58 & 2.61 \\  & & 7 & 70 & 2.58 & 2.61 \\  & & 8 & 80 & 2.55 & 2.61 \\  & & 9 & 90 & 2.60 & 2.61 \\  & & 10 & 100 & 2.60 &