# 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  
In the following steps, we describe the practical implementation of the proposed Hexagonal Fuzzy TOPSIS Method steps that are described in Section 5.2. We use the same use case described in Section 6.1. **Step 1: Construct the fuzzy decision matrix \(M\). **  
As depicted in Figure 10, the use case involves 16 criteria/indicators/factors and 23 actions. We compute the combinatorial weights (\(W_{i}\)), for \(i\in[0,15]\) which refer to the weight of the impact of each vulnerability CVSS factor/indicator and other dynamic 5G network factors, see Table 5, where \(i\) refers to the index of the factor. Further, \(A_{0}\), \(A_{2}\),..., \(A_{22}\) refer to the alternative attacker's actions associated with the consequences of changing the CVSS and dynamic network factors. We set the initial weights based on their factors' impact on the security, latency, and stability of the 5G network, as Table 5 depicts. The criteria and alternative attacker's actions are compared with linguistic terms as Tables 6 and 7 depict. The rating of the alternative attacker's actions given in Table 7 is computed based on the weight/impact of the CVSS and dynamic 5G network factors/indicators on the attackers' actions based on the generated attack graph in Figure 10. For instance, \(w_{1}\), \(w_{5}\), and \(w_{11}\) have a Very High (VH) impact on Action 3 (\(A_{3}\)) because there is a direct impact of indicators 1, 5, and 11 on \(A_{3}\). Similarly, \(w_{13}\) and \(w_{14}\) have Medium-High (MH) impact on \(A_{3}\) because there is an indirect impact of indicators 13 and 14 on \(A_{3}\) through indicator 5. \(W_{3}\) has Low (L) impact on \(A_{3}\) because there is an indirect impact of indicators 3 on \(A_{3}\) through a longer path (I3-A15-I8-A20-I5-A3). Figure 11: The \(I\), \(S\), and \(P\) attack costs and paths. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criteria/Indicators/Factors** & \(W_{i}\) & **Criteria/Indicators/Factors** & \(W_{i}\) & **Criteria/Indicators/Factors**\(W_{i}\) \\ \hline Access Vector 000 & \(W_{0}=0.03\) & Report Confidence 006 & \(W_{6}=0.01\) & Speed 012 & \(W_{12}=0.08\) \\ \hline Access Complexity 001 & \(W_{1}=0.04\) & Collateral Damage 007 & \(W_{7}=0.06\) & Bandwidth 013 & \(W_{13}=0.08\) \\ \hline Authentication 002 & \(W_{2}=0.09\) & Target Distribution 008 & \(W_{8}=0.01\) & Data Size 014 & \(W_{14}=0.08\) \\ \hline Confidentiality impact 003 & \(W_{3}=0.09\) & Confidentiality req. 009 & \(W_{9}=0.09\) & Retainability 015 & \(W_{15}=0.03\) \\ \hline Exploitability 004 & \(W_{4}=0.11\) & Integrity req. 010 & \(W_{10}=0.09\) & - & - \\ \hline Remediation level 005 & \(W_{5}=0.02\) & Availability req. 011 & \(W_{11}=0.09\) & - & - \\ \hline \hline \end{tabular}
\end{table} 
Table 5: The combinatorial weights of the CVSS and dynamic 5G network factors. **Step 4: Calculate the positive and the negative alternatives. **  
Computing the positive and negative ideal solution using Equations (14) and (15), respectively. Using the weighted normalized decision matrix of Table 10, we compute the positive and negative ideal solutions as the largest and smallest HFN of each column of the indicator's weights respectively. For simplicity, we consider the first six factors only, which are \(w_{0}\), \(w_{1}\), \(w_{2}\), \(w_{3}\), \(w_{4}\), and \(w_{6}\). See Table 11.  
**Step 5: Determine the distance measures to ideal solutions. **  
The distance of each alternative from positive and negative ideal is calculated using Equations (14) and (15), then using Equations (16) and (17).