# Modeling and Analysis of New Hybrid Clustering Technique for Vehicular Ad Hoc Network
## 3 Clustering Model
### Covering Rough Set Model  
[PERSON] [8] proposed a classical rough set based on the equivalence relation or segmentation of U, where the equivalence relation was changed to cover U in a CRS. The most important aspects of the rough set are the lower approximations, and the upper approximations of set X are shown in Figure 3.  
The main goal of a CRS is to achieve a reasonable set of approximations and to reduce the number of attributes. The covering process is carried out based on symmetric relations, and distinctive reflexive relations are used to select the most useful vehicle states. Initially, an equivalence relation is created for the covering with the property that two elements intersect the union of finite element covering. A rough set is used to extract the rules and perform attribute reduction by partitions. Although CRS theory achieves the same function, the attributes are described by covers [25].  
**The steps of the rough set are as follows:**  
* Create an information table, which includes the general simulation parameters.
* Calculate the equivalence partition or relation for covering objects (denoted in this work by CG1, CG2, CG3,... CGn).
* Build the covering key of lower approximation for the given information table: \[\underline{GL}(X)=\{k(x)\in GL:k(x)\subseteq X\}\] (1)
* Build the covering key of the upper approximation for the given information table: \[\overline{GL}(X)=\{\cup\{\cap\{k\in GL/x\in k(x)\}/x\in X\}\}\] (2)
* Use CRS to build a certain rule based on (1).
* Use CRS to build possible rules based on (2).
* Eliminate an equivalent rule for covering approximations based on (3): \[BNR=\underline{GL}(X)-\overline{GL}(X)\] (3)
* Finally, calculate the validation measures, choose an appropriate group, and select the road sector.  
Figure 4 shows the rough set system model that was used to collect vehicle groups.  
Figure 3: Rough sets and set approximation.  
CG1 = {G1, G3, G6, G10} \(\cap\) {G1, G3, G5, G7, G10} \(\cap\) {G1, G6, G7, G10} \(=\) {G1, G10} CG2 = Low \(\cap\) Left \(\cap\) Near CG2 = {G2, G7, G8} \(\cap\) {G2, G4, G6, G8, G9} \(\cap\) {G2, G3, G4, G5, G8, G9} = {G2, G8} CG3 = Medium \(\cap\) Right \(\cap\) Near CG3 = {G1, G3, G6, G10} \(\cap\) {G1, G3, G5, G7, G10} \(\cap\) {G2, G3, G4, G5, G8, G9} = {G3} CG4 = High \(\cap\) Left \(\cap\) Near CG4 = {G4, G5, G9} \(\cap\) {G2, G4, G6, G8, G9} \(\cap\) {G2, G3, G4, G5, G8, G9} = {G4, G9} CG5 = High \(\cap\) Right \(\cap\) Near CG5 = {G4, G5, G9} \(\cap\) {G1, G3, G5, G7, G10} \(\cap\) {G2, G3, G4, G5, G8, G9} = {G5} CG6 = Medium \(\cap\) Left \(\cap\) Far CG6 = {G1, G3, G6, G10} \(\cap\) {G2, G4, G6, G8, G9} \(\cap\) {G1, G6, G7, G10} = {G6} CG7 = Low \(\cap\) Right \(\cap\) Far CG7 = {G2, G7, G8} \(\cap\) {G1, G3, G5, G7, G10} \(\cap\) {G1, G6, G7, G10} = {G7} CG8 = Low \(\cap\) Left \(\cap\) Near CG8 = {G2, G7, G8} \(\cap\) {G2, G4, G6, G8, G9} \(\cap\) {G2, G3, G4, G5, G8, G9} = {G2, G8} CG9 = High \(\cap\) Left \(\cap\) Near CG9 = {G4, G5, G9} \(\cap\) {G2, G4, G6, G8, G9} \(\cap\) {G2, G3, G4, G5, G8, G9} = {G4, G9} CG10 = Medium \(\cap\) Right \(\cap\) Far CG10 = {G1, G3, G6, G10} \(\cap\) {G1, G3, G5, G7, G10} \(\cap\) {G1, G6, G7, G10} = {G1, G10} = {G1, G10, G11, G12, G13, G14, G15, G16, G17, G10} = {G1, G10} \end{table}
Table 3: Set of vehicle cases.  
\[\overline{GL}(X)=\left\{\begin{array}{ll}\{G1,\ G2,\ G3,\ G4,\ G5,\ G8,\ G9,\ G10\},& \mbox{Current Sector}\\ \{G1,\ G2,\ G4,\ G6,\ G7,\ G8,\ G9,\ G10\},&\mbox{Next Sector}\end{array}\right. \tag{8}\]  
By applying (3), we can compute the boundary region (BNR), as shown in (9):  
\[BNR=\{G1,\ G2,G4,\ G8.\ G9.G10\} \tag{9}\]  
The covering distribution is illustrated in Figure 5. Groups 1, 2, 4, 8, 9, and 10 are in the boundary region. The pairs {G1, G10}, {G2, G8}, and {G4, G9} are in the same featured group, and the clustering algorithm deals with them together.