## 4 Experimental Results and Comments
### Experimental Methods and Results Analysis
As listed in Table 5, the experimental results revealed that the performance index and processing time showed good results in comparison to those of GFM itself. Furthermore, the proposed method has the advantage of showing that it can be explained by simplifying hierarchical models with each of the two inputs. Figure 6: Prediction results for training data (automobile fuel consumption data, P = 6, C = 2, m = 2, flexible generation method). Figure 7: Prediction results for validation data (automobile fuel consumption database, P = 6, C = 2, m = 2, flexible generation method). +++ ==ERROR: No output for this page==
In the case of Boston housing price data, the experimental results showed that the best performance was achieved by each of 24 fuzzy rules (P = 6, C = 4) for seven GFMs with two inputs for hierarchical tree structure. Here, the performance index of the best model in a hierarchical tree structure is 0.4603. The processing time of the proposed method is 1.2834 s. In contrast, the performance index and processing time of GFM itself with 12 inputs are 0.3043 and 1.3417 s, respectively. Although the proposed method has a similar processing time, the performance index of GFM itself was confirmed to have better performance. However, the GFM itself was found to be difficult to obtain an explainable model because the rules were generated with too many inputs. In the case of energy efficiency data, the experimental results showed that the best performance was achieved by each of the 24 fuzzy rules (P = 6, C = 4) for a single GFM with two inputs for a hierarchical tree structure. Here, the performance index of the best model in a hierarchical tree structure is 0.4952. The processing time of the proposed method is 0.2834 s. In contrast, the performance index and processing time of GFM itself with six inputs are 0.4561 and 1.9887 s, respectively. As listed in Table 5, the performance index and processing time showed good results in comparison to those of GFM itself. Furthermore, the proposed CFCM-based MGFM has the characteristics of representing that it can be explained by simplifying hierarchical models with each of the two inputs. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline m & Context & P & C & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{8}{*}{1.5} & \multirow{8}{*}{Uniform} & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.2481 & 0.2718 & 0.2646 & 0.2651 & 0.2549 \\ \cline{3-8}  & & 4 & 0.3917 & 0.3881 & 0.3783 & 0.4073 & 0.4010 \\ \cline{3-8}  & & 5 & 0.3862 & 0.3426 & 0.3659 & 0.3699 & 0.3676 \\ \cline{3-8}  & & 6 & 0.4478 & 0.4412 & 0.4603 & 0.4233 & 0.3852 \\ \cline{3-8}  & & \multirow{2}{*}{Context} & 6 & 2 & 3 & 4 & 5 & 6 \\ \cline{3-8}  & & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.2995 & 0.2966 & 0.2865 & 0.2663 & 0.2860 \\ \cline{3-8}  & & 4 & 0.3765 & 0.3275 & 0.3391 & 0.3477 & 0.3425 \\ \cline{3-8}  & & 5 & 0.3860 & 0.3396 & 0.3908 & 0.3997 & 0.3744 \\ \cline{3-8}  & & 6 & 0.3698 & 0.4054 & 0.3892 & 0.3762 & 0.3348 \\ \hline m & Context & P & C & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{8}{*}{2} & \multirow{8}{*}{Uniform} & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.2836 & 0.2802 & 0.2890 & 0.2834 & 0.3195 \\ \cline{3-8}  & & 4 & 0.3665 & 0.3729 & 0.3901 & 0.3969 & 0.3818 \\ \cline{3-8}  & & 5 & 0.3668 & 0.3462 & 0.3414 & 0.3759 & 0.3304 \\ \cline{3-8}  & & 6 & 0.3208 & 0.3850 & 0.4100 & 0.4161 & 0.4354 \\ \cline{3-8}  & & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.3127 & 0.3237 & 0.3116 & 0.3096 & 0.3310 \\ \cline{3-8}  & & 4 & 0.3921 & 0.3912 & 0.3942 & 0.3945 & 0.3951 \\ \cline{3-8}  & & 5 & 0.3701 & 0.3498 & 0.3630 & 0.3647 & 0.4252 \\ \cline{3-8}  & & 6 & 0.3663 & 0.3749 & 0.3468 & 0.3475 & 0.3679 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Performance index of tree-structured CFCM-based MGFM for validation data (Boston house price data). Figure 8: Prediction results for training data (Boston housing price data, P = 5, C = 5, m = 2, flexible generation method).