# 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
**Case 1** used three clusters in SID, and SID had no overlapping problems. In **Case 1**, SID had outliers and noise. Because different data sets were used, **Case 1** was divided into **Case 1a** and **Case 1b**. **Case 1a** considered the SID with outliers. Figure 3 shows the SID with outliers in **Case 1a**. In order to build the interval data sets, they were herein 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 the intervals specified in [14; 15], respectively. The name and version of the software developed in this paper is Mobile RIPFCM V1.0. The mobile platform displayed in Figure 4 has three subpages, namely the main windows page in (a), the initial results page in (b) and the final results page in (c). The main windows page shows the information on parameters, the initial results page shows the initial state of this case, and the final results page shows the results after the iteration of Algorithm 1. IC is represented as the iterated counter in Figure 4. OFV is represented as the value of the object function in Figure 4. The design of the smart phones shown in Figures 6, 8, 13-16 is the same. The three colors of the center were red, green, and blue on the initial results page. The final results page also used the different colors to represent the results of each class of SID. The parameters of the RIPFCM clustering approach on the Windows mobile phone are \(m=2\), \(\eta=2\), \(q_{1}=0.3\), \(q_{2}=25\), and \(\delta=1.5\), the number of iterations is 300, and the number of clusters (nc) is 3 for **Case 1a**, as shown in Figure 4a. The initial state for the proposed mobile RIPFCM approach is shown in Figure 4b, and the final results are shown in Figure 4c for **Case 1a**. **Case 1b** considered the SID with outliers and noise. Figure 5 shows the SID with outliers and noise for **Case 1b**. The parameters of the RIPFCM approach on the Windows mobile phone are \(m=1.4\), \(\eta=1.7\), \(q_{1}=0.3\), \(q_{2}=18\), and \(\delta=1.6\), the number of iterations is 300, and the nc is 3 for **Case 1b** with noise and outliers, as shown in Figure 6a. The initial state for the proposed mobile RIPFCM approach is shown



**Case 2** used three clusters in SID, and the SID had overlapping problems. In **Case 2**, the SID had outliers and noise. **Case 2**, similar to **Case 1**, was divided into **Case 2a** and **Case 2b** in accordance with the different data sets. **Case 2a** represents SID with outliers. Figure 7 shows the SID with outliers for **Case 2a**. The parameters of the RIPFCM approach on the Windows mobile phone are \(m=2\), \(\eta=1.5\), \(q_{1}=0.5\), \(q_{2}=25\), and \(\delta=0.9\), the number of iterations is 300, and the nc is 3 for **Case 2a**, as shown in Figure 8a. The initial state for the proposed mobile RIPFCM approach is shown n Figure 8b, and the final results are shown in Figure 8c for **Case 2a**. Figure 4: (**a**) The parameters of the main window, (**b**) the initial results window showing symbolic data with the initial center, and (**c**) the final results window showing the results with outliers for **Case 1a**. Figure 5: The SID with outliers and noise for **Case 1b**. **Case 2b** considered SID with outliers and noise, and the SID had overlapping problems. Figure 9 shows the SID with outliers and noise for **Case 2b**. In this case, a numerical example also illustrated the IFCM, IPFCM and RIPFCM under Euclidean distance. We used Matlab to simulate this case. The number of iterations was 300.