# Multi-Layer Attack Graph Analysis in the 5G Edge Network Using a Dynamic Hexagonal Fuzzy Method
## 6 Performance and Accuracy Evaluation: Case Study
### Evaluating the VAA Using the Hexagonal Fuzzy TOPSIS Method
For example, we compute the distance measure \(D_{0}{}^{+}\) to ideal positive solutions for alternative \(A_{0}\) for the first six factors only for simplicity \(w_{0}\), \(w_{1}\), \(w_{2}\), \(w_{3}\), \(w_{4}\), and \(w_{6}\) is computed as follows: \(D_{0}{}^{+}=\sqrt{d((0.0072,\) 0.009, 0.0108, 0.0126, 0.0144, 0.0162), (0.0072, 0.009, 0.0108, 0.0126, 0.0144, 0.0162))^{2}+d((0.0096, 0.012, 0.0144, 0.0168, 0.0192, 0.0216), (0.004, 0.008, 0.0124, 0.0164, 0.0208, 0.0248))^{2}+d((0.0216, 0.027, 0.0324, 0.0378, 0.0432, 0.0486), (0.009, 0.018, 0.0279, 0.0369, 0.0468, 0.0558))^{2}+d((0.0264, 0.033, 0.0396, 0.0462, 0.0528, 0.0594), (0.011, 0.022, 0.0341, 0.0451, 0.0572, 0.0682))^{2}+d((0.0048, 0.006, 0.0072, 0.0084, 0.0096, 0.0108), (0.002, 0.004, 0.0062, 0.0082, 0.0104, 0.0124))^{2}\) = 0.129. In the same way, we compute \(D_{0}{}^{-}=0.0458\) using the negative ideal solutions values in Table 11. In the same way we can compute the other \(D_{i}{}^{+}\) and \(D_{i}{}^{-}\) for all 22 attacker's actions using the 16 indicators, see Table 12.  
**Step 6: Calculate the cost and benefits of the attacker's actions. **  
The cost (\(At_{Cost}\)) and benefits (\(At_{Benefi}\)) of each attacker's action are computed using Equations (18) and (19). See Table 13. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Positive Ideal Solutions** & **Negative Ideal Solutions** \\ \hline \(E^{-}{}_{0}=\) (0.0072, 0.009, 0.0108, 0.0126, 0.0144, 0.0162) & \(E^{-}{}_{0}=\) (0.003, 0.006, 0.0093, 0.0123, 0.0156, 0.0186) \\ \hline \(E^{-}{}_{1}=\) (0.0096, 0.012, 0.0144, 0.0168, 0.0192, 0.0216) & \(E^{-}{}_{1}=\) (0.004, 0.008, 0.0124, 0.0164, 0.0208, 0.0248) \\ \hline \(E^{-}{}_{2}=\) (0.0216, 0.027, 0.0324, 0.0378, 0.0432, 0.0486) & \(E^{-}{}_{2}=\) (0.009, 0.018, 0.0279, 0.0369, 0.0468, 0.0558) \\ \hline \(E^{-}{}_{3}=\) (0.0171, 0.0243, 0.0306, 0.0378, 0.04, 0.0513) & \(E^{-}{}_{3}=\) (0.009, 0.018, 0.0279, 0.0369, 0.0468, 0.0558) \\ \hline \(E^{-}{}_{4}=\) (0.0264, 0.033, 0.0396, 0.0462, 0.0528, 0.0594) & \(E^{-}{}_{4}=\) (0.011, 0.022, 0.0341, 0.0451, 0.0572, 0.0682) \\ \hline \(E^{-}{}_{5}=\) (0.0048, 0.006, 0.0072, 0.0084, 0.0096, 0.0108) & \(E^{-}{}_{5}=\) (0.002, 0.004, 0.0062, 0.0082, 0.0104, 0.0124) \\ \hline \hline \end{tabular}
\end{table} 
Table 11: The positive and negative ideal solution. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Action** & \({D_{i}}^{+}\) & \({D_{i}}^{-}\) & \(At_{Cost}\)(i)** & \(At_{Benefi}\)**(i)** \\ \hline \(A_{0}\) & 0.0111 & 0.0021 & _0.1591_ & _0.8409_ \\ \hline \(A_{1}\) & 0.0092 & 0.0066 & _0.4177_ & _0.5823_ \\ \hline \(A_{2}\) & 0.0071 & 0.0080 & _0.5298_ & _0.4702_ \\ \hline \(A_{3}\) & 0.0080 & 0.0051 & _0.3893_ & _0.6107_ \\ \hline \(A_{4}\) & 0.0086 & 0.0033 & _0.2773_ & _0.7227_ \\ \hline \(A_{5}\) & 0.0114 & 0 & _0.0000_ & _1.0000_ \\ \hline \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) & \(\vdots\) \\ \hline \(A_{22}\) & 0.0098 & 0.0024 & 0.1967 & 0.8033 \\ \hline \hline \end{tabular}
\end{table} 
Table 12: The cost and benefits of the attacker’s actions. **Step 7: Compute the Shortest Attack Path. **  
To compute the shortest attack path, we calculate the total attack cost of all attack actions that form each possible attack path. After that, we rank the attack paths based on the total attack paths costs and select the path with the lowest cost. Table 13 demonstrates how the attack paths costs are calculated for two vulnerability starting points _CVE-2004-0415_ and _CVE2002-0392_. Intuitively, the cost of exploitation of _CVE-2004-0415_ is less expensive than _CVE2002-0392_ for attacks that target the goal 'I: Exploit mobile backhaul network'. So, the attack that is launched from _\"CVE-2004-0415\"_ to exploit the mobile backhaul network is easier and has lower attack efforts than that is initiated from _CVE2002-0392_. However, the cost of exploitation of _CVE2002-0392_ is less expensive than _CVE-2004-0415_ for attacks that target the goal '_S: Access to Shared resources_' or '_P: Accessing the RAN or MEC_'.