## 5 Experiment and Results Analysis
### Experimental Method and Results  
In interval-based IGM, the predictive performance of Cases 1, 2, and 3 according to the segmentation method of the interval existing in the output space is compared and analyzed through the PI approach. The interval-based IGM's performance was verified through the PI method using the property of coverage and specificity described in Section 4. The experiments were performed as the number of intervals in the interval-based IGM increases from 2 to 10. In addition, the number of clusters per each interval was increased from 2 to 10, and the weighting exponent was fixed at 2. The experiments were performed in Cases 1, 2, and 3. Tables 1 and 2 show the experimental results for Case 1, which is a method of equally dividing the interval without any overlapping. As a result of Case 1, the number of intervals was found to be 7. We selected 10 clusters in each interval, which was approximately 0.39, showing the best result. Figure 10 shows the output value for Case 1 and the actual output value, and Figure 11 shows the PI  
Figure 9: Relation between coverage and specificity. Tables 5 and 6 show the experimental results for Case 3, which is a method of evenly dividing the intervals with overlapping. As a result, the number of intervals was found to be 5. We selected 10 clusters in each interval, which was approximately 0.44, thus yielding the best result. Figure 14 visualizes the output value for Case 2 and the actual output value, and Figure 15 shows the PI value for Case 2 in the form of a mesh. Figure 12: Prediction results for interval-based IGM (Case2). Figure 13: Results of PI method for interval-based IGM (Case 2). Figure 14: Prediction results for interval-based IGM (Case 3). \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**I** & **C** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
**2** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**3** & 0.250 & 0.260 & 0.258 & 0.261 & 0.257 & 0.261 & 0.260 & 0.263 & 0.260 \\
**4** & 0.383 & 0.398 & 0.394 & 0.400 & 0.406 & 0.407 & 0.408 & 0.407 & 0.413 \\
**5** & 0.386 & 0.396 & 0.396 & 0.406 & 0.417 & 0.432 & 0.431 & 0.432 & 0.436 \\
**6** & 0.352 & 0.385 & 0.390 & 0.397 & 0.391 & 0.399 & 0.408 & 0.423 & 0.419 \\
**7** & 0.339 & 0.363 & 0.357 & 0.361 & 0.342 & 0.361 & 0.370 & 0.378 & 0.387 \\
**8** & 0.310 & 0.321 & 0.327 & 0.321 & 0.321 & 0.332 & 0.346 & 0.366 & 0.369 \\
**9** & 0.281 & 0.280 & 0.288 & 0.310 & 0.298 & 0.309 & 0.310 & 0.314 & 0.325 \\
**10** & 0.250 & 0.277 & 0.275 & 0.278 & 0.288 & 0.282 & 0.296 & 0.313 & 0.323 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: CCS prediction results for interval-based IGM (Case 3) using training data. \begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**I** & **C** & **2** & **3** & **4** & **5** & **6** & **7** & **8** & **9** & **10** \\ \hline
**2** & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 & 0 \\
**3** & 0.310 & 0.313 & 0.317 & 0.319 & 0.319 & 0.320 & 0.321 & 0.323 & 0.324 \\
**4** & 0.414 & 0.417 & 0.424 & 0.417 & 0.426 & 0.428 & 0.435 & 0.432 & 0.441 \\
**5** & 0.414 & 0.414 & 0.417 & 0.418 & 0.427 & 0.435 & 0.431 & 0.439 & 0.443 \\
**6** & 0.383 & 0.400 & 0.399 & 0.400 & 0.396 & 0.405 & 0.419 & 0.432 & 0.416 \\
**7** & 0.356 & 0.369 & 0.367 & 0.363 & 0.370 & 0.370 & 0.373 & 0.383 & 0.390 \\
**8** & 0.330 & 0.335 & 0.338 & 0.336 & 0.327 & 0.336 & 0.330 & 0.359 & 0.335 \\
**9** & 0.304 & 0.298 & 0.300 & 0.303 & 0.295 & 0.306 & 0.301 & 0.300 & 0.309 \\
**10** & 0.276 & 0.314 & 0.296 & 0.301 & 0.301 & 0.289 & 0.291 & 0.281 & 0.294 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: CCS prediction results for interval-based IGM (Case 3) using testing data. Table 7 lists the excellent prediction results obtained for each interval-based IGM. Case 1 and 2 showed good performance when the numbers of intervals and clusters were 7 and 10, respectively, and generated 70 rules. Case 3 showed good performance when the numbers of intervals and clusters were 5 and 10, respectively.