## 4 Experimental Results and Comments
### Experimental Methods and Results Analysis
As in the previous experiment, the specificity is not secured when the number of contexts is set to 2, and the resulting specificity value is close to 0. Hence, the performance index is 0. Figures 8 and 9 show the prediction results for the training data and validation data, respectively. As shown in these figures, it was confirmed that tree-structured CFCM-based MGFM showed valid prediction performance for Boston housing data. Table 5 lists the experimental results for the automobile fuel consumption prediction, the Boston housing price prediction, and the additional energy efficiency example. Figure 10 shows the performance comparison for CFCM-based MGFM and GFM itself. As listed in Table 5, the experimental results for the automobile fuel consumption data demonstrated that the best performance was achieved by each of 18 fuzzy rules (P = 6, C = 3) for four GFMs with two inputs for hierarchical tree structure. Here, the performance index of the best model in a hierarchical tree structure is 0.4909. The processing time of the proposed method is 0.0104 s. In contrast, the performance index and processing time of GFM itself with six inputs are 0.3986 and 0.4 s, respectively. Here, the number of premise and \begin{table}
\begin{tabular}{c c c c c c c c} \hline m & Context & P & C & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{8}{*}{1.5} & \multirow{8}{*}{Uniform} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} \\ \cline{3-3} \cline{5-8}  & & & 2 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & & 3 & 0.2493 & 0.2766 & 0.2808 & 0.2966 & 0.2747 \\ \cline{3-8}  & & & 4 & 0.3915 & 0.3568 & 0.3854 & 0.3833 & 0.3573 \\ \cline{3-8}  & & & 5 & 0.4505 & 0.3713 & 0.3921 & 0.4036 & 0.4398 \\ \cline{3-8}  & & & 6 & 0.4538 & 0.4602 & 0.4559 & 0.4060 & 0.4247 \\ \cline{3-8}  & & & 2 & 3 & 4 & 5 & 6 \\ \cline{3-8}  & & & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & & 3 & 0.2696 & 0.2620 & 0.2132 & 0.2714 & 0.3021 \\ \cline{3-8}  & & & 4 & 0.3860 & 0.3593 & 0.3432 & 0.3509 & 0.3809 \\ \cline{3-8}  & & & 5 & 0.4098 & 0.4505 & 0.4110 & 0.4170 & 0.3844 \\ \cline{3-8}  & & & 6 & 0.4055 & 0.4408 & 0.4080 & 0.4090 & 0.3865 \\ \hline m & Context & P & C & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{8}{*}{2} & \multirow{8}{*}{Uniform} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} \\ \cline{3-8}  & & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & & 3 & 0.3001 & 0.2874 & 0.2909 & 0.2805 & 0.2962 \\ \cline{3-8}  & & 4 & 0.4068 & 0.4149 & 0.3938 & 0.4254 & 0.4290 \\ \cline{3-8}  & & 5 & 0.4641 & 0.4599 & 0.4435 & 0.4600 & 0.4513 \\ \cline{3-8}  & & 6 & 0.4553 & 0.4737 & 0.4530 & 0.4479 & 0.4710 \\ \cline{3-8}  & & & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{8}{*}{2} & \multirow{8}{*}{Context} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} & \multirow{8}{*}{1.5} \\ \cline{3-8}  & & 3 & 0.2935 & 0.2837 & 0.3133 & 0.3320 & 0.2877 \\ \cline{1-1} \cline{3-8}  & & 4 & 0.4395 & 0.4266 & 0.4178 & 0.4270 & 0.4334 \\ \cline{1-1} \cline{3-8}  & & 5 & 0.4458 & 0.4610 & 0.4351 & 0.4850 & 0.4734 \\ \cline{1-1} \cline{3-8}  & & 6 & 0.4597 & 0.4909 & 0.4798 & 0.4864 & 0.4724 \\ \hline \end{tabular}
\end{table} 
Table 2: Performance index of tree-structured CFCM-based MGFM for verification data (automobile fuel consumption data). consequent parameters in the explainable simple GFM are 36 (18 centers \(\times\) 2 inputs) and 18 (6 contexts \(\times\) 3 points), respectively. In contrast, the number of the premise and consequent parameters in the GFM itself, which is difficult to explain, are 108 (18 centers \(\times\) 6 inputs) and 18 (6 contexts \(\times\) 3 points), respectively. The experiment was performed with MATLAB 2022a in a desktop environment of Intel Core i7-7700 CPU, RAM 16 GB, NVIDIA Geforce GTX 1060.