## 4 Experimental Results and Comments
### Experimental Methods and Results Analysis  
The performance used in this paper is evaluated by the performance index method, as explained in the previous section. This database was normalized to a value between 0 and 1. Total data are divided by training data (50%) and testing data (50%). The experiment was conducted by increasing the number of contexts (P) and clusters (C) from two to six in each tree-structured CFCM-based MGFM. Furthermore, fuzzification coefficients of 1.5 and 2 were used in the experiment. In addition, the contexts are generated by a uniform and flexible method. In the case of the automobile fuel efficiency prediction experiment, Tables 1 and 2 list the performance index of the tree-structured CFCM-based MGFM with uniformly generated contexts for the training data and validation data, respectively. Here, \(m\) denotes the fuzzification coefficient, and \(P\) and \(C\) represent the number of contexts and clusters, respectively. In addition, \(PI\) denotes the performance index. As listed in Table 2, the best prediction performance is achieved when four contexts and four clusters are created. However, when the context's number is set to 2, the specificity of the information granules is not secured, and the specificity value is close to 0. Consequently, the performance index is 0. Figures 6 and 7 show the prediction results for the training data and validation data, respectively. In these figures, the solid black line represents the actual output values of the data, and the dotted red line represents the predicted values of the proposed method. As shown in these figures, the experimental results revealed that tree-structured CFCM-based MGFM showed good prediction performance for automobile fuel consumption data. \begin{table}
\begin{tabular}{c c c c c c c c} \hline m & Context & P & C & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{5}{*}{1.5} & \multirow{5}{*}{Uniform} & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.2687 & 0.2701 & 0.2855 & 0.3002 & 0.2826 \\ \cline{3-8}  & & 4 & 0.3647 & 0.3690 & 0.3838 & 0.3790 & 0.3431 \\ \cline{3-8}  & & 5 & 0.4600 & 0.4101 & 0.4177 & 0.4143 & 0.3932 \\ \cline{3-8}  & & 6 & 0.4526 & 0.4651 & 0.4304 & 0.3800 & 0.4182 \\ \cline{3-8}  & & \multirow{5}{*}{Context} & \multirow{5}{*}{P} & C & & & & \\ \cline{3-8}  & & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.2871 & 0.2597 & 0.2246 & 0.2805 & 0.3187 \\ \cline{3-8}  & & 4 & 0.3893 & 0.3701 & 0.3843 & 0.3690 & 0.3533 \\ \cline{3-8}  & & 5 & 0.4105 & 0.3902 & 0.4050 & 0.4099 & 0.3793 \\ \cline{3-8}  & & 6 & 0.4346 & 0.4419 & 0.3970 & 0.3890 & 0.3915 \\ \hline m & Context & P & C & 2 & 3 & 4 & 5 & 6 \\ \hline \multirow{5}{*}{Uniform} & \multirow{5}{*}{Uniform} & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.3027 & 0.2907 & 0.2945 & 0.3069 & 0.3115 \\ \cline{3-8}  & & 4 & 0.4294 & 0.4017 & 0.4014 & 0.3759 & 0.3828 \\ \cline{3-8}  & & 5 & 0.4278 & 0.4028 & 0.4481 & 0.4036 & 0.4165 \\ \cline{3-8}  & & 6 & 0.4091 & 0.4445 & 0.4447 & 0.4213 & 0.4619 \\ \cline{3-8}  & & 2 & 0 & 0 & 0 & 0 & 0 \\ \cline{3-8}  & & 3 & 0.3248 & 0.3184 & 0.2914 & 0.3055 & 0.3004 \\ \cline{3-8}  & & 4 & 0.4494 & 0.4301 & 0.4605 & 0.4197 & 0.4520 \\ \cline{3-8}  & & 5 & 0.4771 & 0.4160 & 0.4203 & 0.4689 & 0.4453 \\ \cline{3-8}  & & 6 & 0.4219 & 0.4416 & 0.4311 & 0.4534 & 0.4258 \\ \hline \end{tabular}
\end{table} 
Table 1: Performance index of tree-structured CFCM-based MGFM for training data (automobile fuel consumption data). In what follows, we performed the experiments for the Boston housing price prediction. Tables 3 and 4 list the performance index of the tree-structured CFCM-based MGFM for the training data and verification data, respectively. In the same manner, the experiment was conducted by increasing the number of contexts and clusters from two to six in each tree-structured CFCM-based MGFM. As listed in Table 4, the best performance is achieved when three contexts and four clusters are created.