# Connectivity Maintenance Based on Multiple Relay UAVs Selection Scheme in Cooperative Surveillance
## 3 Multiple Relay UAVs Selection Scheme Based on Fuzzy Optimum Selection
### Membership Degree of UAV Alternatives Assessment Based on Fuzzy Optimum Selection  
With motion of UAVs, it is obvious that UAV importance changes dynamically in communication network. As a multi-attributed decision making problem, the membership degree to the ideal optimum alternative of multiples UAV is considered as an evaluation indicator for relay selection, which is assessed by fuzzy optimum selection. Correspondingly, multiple relay UAVs are chosen based on the descending membership degree sequence for connectivity maintenance. Combined with the feature of network connectivity in cooperative surveillance, four modified attributes representing differences among UAV alternatives are proposed in this work. It is obvious that the closer UAV to ground station is more critical to maintain connectivity, and vice versa. Firstly, frequent role conversion is not benefit for the continuity of surveillance tasks, therefore maintaining appropriate roles by different role values (RV) are essential for cooperative surveillance tasks. Similar to the shortest path in graph, minimum hops to ground station (MH) corresponds to the shortest end-to-end communication channel, which effectively reduce surveillance information delay and improve the reliability [28]. The ratio of minimum hops channels via current UAV between all UAVs and ground station (RMH) is similar to all shortest paths that travel through the same one node in graph, which reflects the influence of current UAV on others' communication with ground station. In some extreme situations, it is not explicit to distinguish UAV alternatives with the same role. For the purpose of overcoming the shortage, actual distance to ground station (AD) is a complementary factor. Thus, four attributes comprised of role values, minimum hops to ground station, the ratio of minimum hops channels via current UAV between all UAVs and ground station, and actual distance to ground station, namely RV, MH, RMH and AD, are employed to assessing UAV alternatives in cooperative surveillance. The attributes are described as follows:  
\[RV(i)=\left\{ \begin{array}{l}1,\;UAV\;i\;\text{is a SUAV}\\ 2,\;UAV\;i\;\text{is a AUAV}\\ 3,\;UAV\;i\;\text{is a RUAV}\end{array} \right. \tag{10}\]  
\[MH(i)=\underset{x_{i}\in\Omega_{i}}{\text{min}}H(x_{i}) \tag{11}\] \begin{table}
\begin{tabular}{c c c} \hline \hline
**Role** & **Task** & **Role Description** \\ \hline \hline RUAV & preserving communication connection & constructing relay communication links \\ \hline \hline AUAV & connecting RUAV and SUAVs swarm & balancing surveillance mission and \\ \hline SUAV & searching and detecting unknown region & maximizing surveillance payoff \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Three UAV roles in cooperative surveillance with ground station. \[RMH(i)=\sum_{i\
eq j,i\in U}\frac{H_{ji}}{H_{j}} \tag{12}\]  
\[AD(i)=\sqrt{\left(x_{i}-x_{b}\right)^{2}+\left(y_{i}-y_{b}\right)^{2}} \tag{13}\]  
In Equations (10)-(13), \(i\) is the UAV identification. Equation (10) reflects different UAV role values in cooperative surveillance, and the minimum hops to ground station of UAV \(i\) is described as Equation (11), where \(\Omega_{i}\) is the set of all communication channels between UAV \(i\) and ground station. \(\mathbf{x}_{i}\) is the communication channel between UAV \(i\) and ground station, and \(H(\mathbf{x}_{i})\) is the hop counts of \(\mathbf{x}_{i}\). The ratio of minimum hops channels via current UAV between all UAVs and ground station is denoted as Equation (12), where \(H_{j}\) is the number of communication channels between UAV \(j\) and ground station with minimum hops, and \(H_{ji}\) is the number of minimum hops channels via UAV \(i\). For connectivity maintenance, some UAVs should serve as relays to dynamically establish communication links, and relevant relay UAVs are chosen by fuzzy optimum selection according to four attributes mentioned above, which can be considered as the objectives to identify an optimum alternative from \(N_{U}\) UAVs.