## 4 Experiments and Result Analysis
### Experiment Method and Result Analysis  
This study evaluates the prediction performance through the PI method, which is a performance evaluation method that is suitable for the IG and fuzzy granular model, instead of the generally used performance evaluation methods. As shown in Equation (20), the PI is expressed by the multiplication of coverage (\(\varepsilon\)), which is the coverage of IG, and specificity (\(\varepsilon\)), which is the specificity of IG. A value closer to 1 indicates higher performance. The experiment method is as follows. Each benchmarking database was divided into 50% for training and 50% for validation, and the PI was normalized to a value between 0 and 1. Experiments were conducted as the numbers of context (P) and cluster (C) of the CGK-GM, AGM, and the proposed Optimal CGK-GM and Optimal AGM were increased from 2 to 6. The fuzzy factor was fixed to 2. Furthermore, the two methods of generating contexts in  
Figure 8: Structure of the optimized CGK-based fuzzy granular model of the aggregated structure. the output space, i.e., uniform and flexible generation methods, were compared. The GA used for context optimization was experimented with using the number of generations to 540, the cross-operation ratio of 0.97, and the mutation rate of 0.01. \[Performance\ index=coverage(\varepsilon)\cdot\ specificity(\varepsilon) \tag{20}\]  
The following shows the result of the concrete compressive strength prediction experiment. Table 1 shows the prediction performance of the CGK-based fuzzy granular model that generated contexts uniformly. Table 2 shows the prediction performance of the CGK-based fuzzy granular model that generated contexts flexibly. Tables 1 and 2 show that the higher the context, the higher the performance. The highest performance with a PI of 0.470 was achieved when the uniform generation method, six contexts, and four clusters were used. Figure 9 shows the output of the CGK-based fuzzy granular model and the real output. Figure 10 shows the PI of the CGK-based fuzzy granular model for the testing data. In Figure 9, the \(x\)-axis shows the number of concrete compressive strength, and the \(y\)-axis shows the concrete compressive strength. The solid black line indicates the real concrete compressive strength, whereas the red dotted line indicates the output of the CGK-based fuzzy granular model. In Figure 10, the \(x\)-axis shows the number of clusters generated in the input space, the \(y\)-axis shows the number of contexts generated in the output space, and the \(z\)-axis shows the PI for the validation data. Experiments were performed on the Windows 10 operating system, and the software used is MATLAB 2018a. Figure 11 shows the output of the CGK-based fuzzy granular model of the aggregated structure and the real output. Figure 12 shows the PI of the CGK-based fuzzy granular mode for validation data. Figure 10: Performance index of the CGK-based fuzzy granular model for testing data (uniform generation of contexts, number of contexts = 6, number of clusters = 4). Figure 9: Comparison of the output of the CGK-based fuzzy granular model and real output (uniform generation of contexts, number of contexts = 6, number of clusters = 4). \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**P** & **C** & **2** & **3** & **4** & **5** & **6** \\ \hline
2 & 0 & 0 & 0 & 0 & 0 \\ \hline
3 & 0.0481 & 0.0437 & 0.0446 & 0.0391 & 0.0451 \\ \hline
4 & 0.3071 & 0.3023 & 0.3136 & 0.3187 & 0.3129 \\ \hline
5 & 0.4344 & 0.4348 & 0.4380 & 0.4471 & 0.4418 \\ \hline
6 & 0.4884 & 0.4981 & 0.4921 & 0.5074 & 0.5028 \\ \hline \end{tabular}
\end{table} 
Table 4: Prediction performance CGK-based fuzzy granular model of the aggregated structure that generated contexts flexibly. Figure 11: Comparison between the output of the CGK-based fuzzy granular model of the aggregated structure and the real output (uniform generation of contexts, number of contexts = 6, number of clusters = 4).