## 5 Simulation Results
\begin{table}
\begin{tabular}{c c c c c} \hline \hline  & \multicolumn{3}{c}{**(a)**} \\ \hline
**Compared Index/Method** & \begin{tabular}{c} **IFCME** \\ **(\(m=2\))** \\ \end{tabular} & \begin{tabular}{c} **IIFPFCME** \\ **(\(\eta=0.01\))** \\ \end{tabular} & \
\begin{tabular}{c} **IIFPFCME** \\ **(\(\eta=0.1\))** \\ \end{tabular} &
\begin{tabular}{c} **IIFPFCME** \\ **(\(\eta=1\))** \\ \end{tabular} \\ \hline RMSE & 0.1871 & 0.1778 & 0.1780 & 0.1810 \\ \hline Average times on ten (sec.) & 0.004011 & 0.001845 & 0.002007 & 0.002452 \\ \hline Average number of ten iterations (\(l\)) & 22.1 & 8.4 & 9.3 & 11.7 \\ \hline \hline \multicolumn{5}{c}{(b)} \\ \hline
**Compared Index/Method** & \begin{tabular}{c} **IFCMC** \\ **(\(m=2\))** \\ \end{tabular} & \begin{tabular}{c} **IIFPFCMC** \\ **(\(\eta=0.01\))** \\ \end{tabular} & \
\begin{tabular}{c} **IIFPFCMC** \\ **(\(\eta=0.1\))** \\ \end{tabular} &
\begin{tabular}{c} **IIFPFCMC** \\ **(\(\eta=1\))** \\ \end{tabular} \\ \hline RMSE & 0.6437 & 0.0522 & 0.0522 & 0.0522 \\ \hline Average times on ten (sec.) & 0.008791 & 0.006091 & 0.005886 & 0.006728 \\ \hline Average number of ten iterations (\(l\)) & 12.6 & 8.1 & 7.8 & 9 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The results of the comparison for IDS5 with different approaches: (**a**) using IFCME and IIFPFCME under different \(\eta\); and (**b**) using IFCMC and IIFPFCMC under different \(\eta\). The second dataset (DS2) with 243 points was constructed using DS1 and another one-point (14, 4) outlier, as shown in Figure 9a. On the other hand, the interval datasets of DS2 (IDS2) are shown in Figure 9b. In this case, the symbolic data with outliers were illustrated as powerful via the proposed IIFPFCMC method. The results of IFCME and IFCMC with \(m=2\) for IDS2 are shown in Figure 10. The results of IIFPFCME and IIFPFCMC with parameters \(\eta=0.01\) and \(\eta=0.1\) for IDS2 are shown in Figures 11 and 12, respectively. The results of IPFCME for IDS2 are shown in Figure 13. The results of the comparison are shown in Table 2. From Table 2, the proposed IIFPFCME and IIFPFCMC on performance and average times are all better than IFCME, IFCMC, and IPFCME. From Table 2, the proposed IIFPFCMC is better than the proposed IIFPFCME under a symbolic set with outliers. From Figure 10, the clustering results are not good, as the  
The results of IFCME and IFCMC with parameter \(m=2\) for IDS3 are shown in Figure 15. The results of IIFPFCME and IIFPFCMC with parameters \(\eta=0.01\) and \(\eta=0.1\) for IDS3 are shown in Figures 16 and 17, respectively. The results of the comparison are shown in Table 3. From Table 3, the proposed IIFPFCME and IIFPCMC on performance and average times are all better than IFCME, IFCMC, and IPFCME. From Table 3, the proposed IIFPFCMC is better than the proposed IIFPFCME under a symbolic set with more outliers and different positions. The fourth dataset (DS4) with 249 points consists of five clusters whose centers are (1, 1), (1, 9), (9, 1), (5, 5), and (9, 9) and diamond shapes on each group. For the first four clusters, the number of data points per cluster was 41 data points. For the last cluster centered at (9, 9), there were 85 data points (see Figure 18a); that is, DS4 used large and small groups and diamond shapes on each group to demonstrate the advantages of the proposed method. In order to build the interval datasets, this was defined as \(([21-\gamma_{1}/2,z1+\gamma_{1}/2],[22-\gamma_{2}/2,z2+\gamma_{2}/2])\), from which \(\gamma_{1}\) and \(\gamma_{2}\) were drawn randomly from [0.2, 1] (see Figure 18b). The results of IFCME and IFCMC with parameter \(m=2\) for IDS4 are shown Figure 19. The results of IIFPFCME and IIFPFCMC with parameters \(\eta=0.01\) and \(\eta=0.1\) for IDS4 are shown Figures 20 and 21, respectively. Table 4 shows the results of the comparison for IDS4 with different approaches, namely IFCME, IIFPFCME under different \(\eta\), IFCM, and IIFPFCMC under different \(\eta\).