## 5 Simulation Results
From Table 4, the proposed IIFPFCME and IIFPFCMC on performance and average times are all better than IFCME and IFCMC. From Table 4, the  
Figure 14: (**a**) The third dataset (DS3) and (**b**) interval datasets of DS3 (IDS3). Figure 13: The results of the IPFCME parameter with (**a**) \(m=1.5,\ n=2,\ a=20,\ b=50\) and (**b**) \(m=1.5,\ n=2,\ a=50,\ b=50\) for IDS2. The fifth dataset (DS5) with 252 points were constructed using DS4 and another one-point (14, 4) outlier, as shown as Figure 22a. On the other hand, the interval datasets of DS5 (IDS5) are shown in Figure 22b; that is, IDS5 used large and small groups, outliers, and diamond shapes on each group to demonstrate the advantages of the proposed method. Figure 19: The results of the (**a**) IFCME and (**b**) IFCMC parameters with \(m=2\) for IDS4. Figure 10.0 The results of the IIFPFCME parameter with (**a**) \(\eta=0.01\) and (**b**) \(\eta=0.1\) for IDS4. The results of IFCME and IFCMC with parameter \(m=2\) for IDS5 are shown in Figure 10.1 The results of IIFPFCME and IIFPFCMC with parameters \(\eta=0.01\) and \(\eta=0.1\) for IDS5 are shown in Figures 24 and 25, respectively. Table 5 shows the results of the comparison for IDS5 with different approaches, namely IFCME, IIFPFCME under different \(\eta\), IFCMC, and IIFPFCMC under different \(\eta\). From Table 5, the proposed IIFPFCME and IIFPFCMC on performance and average times are all better than IFCME and IFCMC. From Table 5, the proposed IIFPFCMC is better than the proposed IIFPFCME under a symbolic set of large and small groups, outliers, and diamond shapes on each group on the RMSE. The sixth dataset (DS6) with 261 points were constructed using DS4 and added four points, namely (14, 6), (6, 14), (6, \(-\)4), and (\(-\)4, 6), as shown as Figure 26a. On the other hand, the interval datasets of DS6 (IDS6) are shown in Figure 26b. That is, IDS6 used large and small groups, more outliers, and diamond shapes on each group to demonstrate the advantages of the proposed method. The results of IFCME and IFCMC with parameter \(m=2\) for IDS6 are shown in Figure 10.2 The results of IIFPFCME and IIFPFCMC with parameters \(\eta=0.01\) and \(\eta=0.1\) for IDS6 are shown in Figures 28 and 29, respectively. Table 6 shows the results of the comparison for IDS6 with different approaches, namely, IFCME, IIFPFCME under different \(\eta\), IFCMC, and IIFPFCMC under different \(\eta\). From Table 6, the proposed IIFPFCME and IIFPFCMC on performance and average times are all better than IFCME and IFCMC. From Table 6, the proposed IIFPFCMC is better than the proposed IIFPFCME under a symbolic set of large and small groups, more outliers, and diamond shapes on each group on the RMSE. Figure 10.3 The results of the IIFPFCMC parameter with (a) \(\eta=0.01\) and (b) \(\eta=0.1\) for IDS4. Figure 10.4 (a) The fifth dataset (DS5) and (b) interval datasets of DS5 (IDS5). We presented two real datasets concerning exchange rates for validation of the proposed methods. The seventh interval dataset (IDS7) represents weekly low- and high-price correlation data for EUR/USD on z2 and TW/USD on z1. The eighth interval dataset (IDS8) represents weekly low- and high-price correlation data for GBP/USD on z2 and TW/USD on z1. For the currency exchange rate dataset, data were collected during a 5-year period  
(2011-2015). For a detailed description of this dataset on currency exchange rates and the results of IFCME, please refer to the study published by the authors of [35]. Figure 10.5 The results of the IIFPFCME parameter with (a) \(\eta=0.01\) and (b) \(\eta=0.1\) for IDS6. Figure 10.6 (**a**) The sixth dataset (DS6) and (**b**) interval datasets of DS6 (IDS6). Figure 10.7 The results of the (**a**) IFCME and (**b**) IFCMC parameters with \(m=2\) for IDS6. The results of IFCMC with parameter \(m=2\) for IDS7 are shown in Figure 30a. The results of IIFPFCMC and IIFPFCMC with parameters \(\eta=1\), \(\eta=0.1\), and \(\eta=0.01\) for IDS7 are shown in Figures 30b-d and 31 respectively.