# Rough IPFCM Clustering Algorithm and Its Application on Smart Phones with Euclidean Distance
## 2 Proposed Rough Interval Possibilistic Fuzzy C-Means Clustering Algorithm with Euclidean Distance
The results of IFCM with parameter \(m=2\) for **Case 2b** are shown on Figure 10. The results of IPFCM with parameters \(m=1.9\), \(\eta=2\), \(q_{1}=1\), and \(q_{2}=25\) for **Case 2b** are shown on Figure 11. The results of RIPFCM with parameters \(m=2\), \(\eta=1.3\), \(q_{1}=0.3\), \(q_{2}=22\), and \(\delta=3.5\) for **Case 2b** are shown on Table 2.0 The RMSE results with IFCM, IPFCM, and RIPFCM under Euclidean distance are shown in Table 2.1

Table 2.2 (**a**) The parameters of the main window, (**b**) the initial results window showing the symbolic data with the initial center, and (**c**) the final results window showing the results with outliers for **Case 1b**. Table 2.3 The SID with outliers for **Case 2a**. In this case, the parameters of the RIPFCM approach on the Windows mobile phone are \(m=2\), \(\eta=1.3\), \(q_{1}=0.3\), \(q_{2}=22\), and \(\delta=3.5\), the number of iterations is 300, and the nc is 3 for **Case 2b** with noise and outliers, as shown in Figure 12(a). The initial state for the proposed mobile RIPFCM approach is shown in Figure 12(b), and the final results are shown in Figure 12(c) for **Case 2b** with noise and outliers. \begin{table}
\begin{tabular}{c c c c} \hline \hline  & **IFCM [9]** & **IPFCM [13]** & **RIPFCM** \\ \hline RMSE & 10.2120 & 4.6490 & 1.1871 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Comparison of RMSE for IDS4 with different approaches. Figure 8: (**a**) The parameters of the main window, (**b**) the initial results window showing the symbolic data with the initial center, and (**c**) the final results window showing the results with outliers for **Case 2a**. Figure 9: The SID with outliers and noise for **Case 2b**. Figure 11: The results of IPFCM with parameters \(m=1.9\), \(\eta=2\), \(q_{1}=1\), and \(q_{2}=25\) for **Case 2b**. Figure 10: The results of IFCM with parameter \(m=2\) for **Case 2b**. **Case 3** used six clusters in SID, and the SID had no overlapping problem. In **Case 3**, the SID had outliers and noise. **Case 3a** considered SID with outliers. The parameters of the RIPFCM approach on the Windows mobile phone are \(m=1.2\), \(\eta=1.5\), \(q_{1}=1\), \(q_{2}=10\), and \(\delta=0.5\), the number of iterations is 300, and the nc is 6 for **Case 3a**, as shown in Figure 13(a). The initial state for the proposed mobile RIPFCM approach is shown in Figure 13(b), and the final results are shown in Figure 13(c) for **Case 3a**. **Case 3b** considered SID with outliers and noise. The parameters of the RIPFCM approach on the Windows mobile phone are \(m=1.2\), \(\eta=2\), \(q_{1}=1\), \(q_{2}=8\), and \(\delta=1.5\)

Figure 14: (**a**) The parameters of the main window, (**b**) the initial results window showing the symbolic data with the initial center, and (**c**) the final results window showing the results with outliers for **Case 3a**. Figure 13



the number of iterations is 300, and the nc is 6 for **Case 3b** with noise and outliers, as shown in Figure 15a. The initial state for the proposed mobile RIPFCM approach is shown in Figure 15b, and the final results are shown in Figure 15c for **Case 3b** with noise and outliers. **Case 4** used six clusters in SID, and the SID had overlapping problems. In **Case 4**, the SID consisted of a data set with outliers and noise for data overlapping problems. The parameters of the RIPFCM approach on the Windows mobile phone are \(m=1.1\), \(\eta=1.4\), \(q_{1}=0.8\), \(q_{2}=11\), and \(\delta=1.2\), the number of iterations is 300, and the nc is 6 for **Case 4** with noise and outliers, as shown in Figure 16a. +++ ==WARNING: Truncated because of repetitions==
**Case 5** used six clusters in SID, and the SID had overlapping problems. In **Case 4**, the SID consisted of a data set with outliers and noise for data overlapping problems. The parameters of the RIPFCM approach on the Windows mobile phone are \(m=1.1\), \(\eta=1.4\), \(q_{1}=0.8\), \(q_{2}=11\), and \(\delta=1.2\), the number of iterations is 300, and the nc is 6 for **Case 4** with noise and outliers, as shown in Figure 16a.