# A Design of CGK-Based Granular Model Using Hierarchical Structure
## 5 Experiment and Results Analysis
### Experimental Method and Results  
In this study, the prediction performance of the granular model was evaluated by the Performance Index (PI) method, which is a performance evaluation method that is suitable for IGs and granular models, rather than the generally used evaluation methods. As expressed in Equation (18). The experiment method is presented as follows. Each database was divided into 50% learning data and 50% validation data, normalized to values between zero and one and then used in the experiments. The numbers of contexts (P) and clusters (C) in conventional GM, the proposed CGK-GM, and AGM were increased from 2 to 6 in increments of 1 during the experiments, while the fuzzification coefficient was fixed at 2. In addition, the experiments were performed using the uniform and flexible method of creating contexts. The following shows the results of the concrete compressive strength prediction experiment. Table 1 shows the prediction performance of the existing GM that created the context uniformly, and Table 2 shows the prediction performance of the GM that created the context flexibly. Figure 16 shows the output value and actual output value of the existing GM, and Figure 17 shows the performance index value of the existing GM for the verification data. In Figure 16, the \(x\)-axis represents the number of verification data for the concrete compressive strength, and the \(y\)-axis represents the concrete compressive strength value. The black solid line is the actual concrete compressive strength value, and the red dotted line shows the output value of the existing GM. As shown in the figure, it can be  
Figure 15: Structure of a CGK granular model with an aggregated structure. Table 3 lists the prediction performance of the CGK-GM in which the contexts are uniformly generated, and Table 4 lists the prediction performance of the CGK-GM in which the contexts are flexibly generated. Figure 18 shows the output and actual output values of CGK-GM, and Figure 19 shows the predictive performance of CGK-GM using performance indicators. As shown in Figure 18, it can be seen that the CGK-GM output value predicts only a large change in the actual output value, but predicts the actual output value more similarly than the conventional GM output value. Figure 19. Shows the performance index values of CGK-GM for the verification data. As shown in the figure,  
Figure 19: CGK-GM’s performance index for validation data (context equally generated, number of contexts = 6, number of clusters = 4). Figure 18: Comparison of the output value of the existing CGK-GM with the actual output value (context is created equally, the number of contexts = 6, the number of clusters = 4). Table 7 shows the experimental results of concrete compressive strength prediction. As shown in the table, it can be seen that the existing GM creates the contexts equally and the performance index value for the verification data is 0.4276 when the context is 6 and the cluster is 6. In this paper, it was confirmed that the proposed methods, CGK-GM and AGM, show better prediction performance than the conventional GM when the contexts are created equally. As an additional experiment, a house price prediction experiment using the Boston house price database [58] was performed. Table 8 shows the experimental results of Boston house price prediction. As a result of the experiment, the existing GM created the context equally in the output space, and when there were 6 contexts and 4 clusters, a value of 0.5431 was obtained. It was confirmed that the proposed method, CGK-GM, generates contexts evenly and shows better performance at 0.5502 when there are 6 contexts and 5 clusters. It can be seen that AGM flexibly creates a context in the output space and shows better prediction performance than the previous model at 0.5870 when there are 3 contexts and 6 clusters. As a result of conducting an experiment using two databases, it was confirmed that the shape of the context created in the output space affects the performance according to the characteristics of the data.