## 3 Road Operational Resilience Evolution Based on DBN
### DBN Parameter Learning Based on Node Resilience Status
Assign confidence between 0 and 1 to focal elements within the identification framework, determining the Basic Probability Assignment or mass function \(\mathrm{m(A)}\) as Equation (6). \[\sum\limits_{\mathrm{A}\leq\Theta}\mathrm{m(A)}=1\] (6) \[\forall\mathrm{A}\subseteq\Theta,0\leq\mathrm{m(A)}\leq 1\]
3. The Dempster-Shafer combination rule is used to combine two independent mass functions. This method gives us the fusion result \(\mathrm{m_{1,2}(A)}\) of the parent node's resilience status and the upper-level node's resilience status. The calculations are as in Equations (7)-(9). \[\mathrm{m_{1,2}(A)}=\mathrm{m_{1}(A)}\oplus\mathrm{m_{2}(A)}\] (7) \[\mathrm{m_{12}(A)}=\left\{ \begin{array}{ll}\frac{\sum_{X\cap Y =\mathrm{A},\forall X\cap Y\in\Theta}\mathrm{m_{1}(X)}\mathrm{m_{2}(Y)}}{1- \mathrm{K}}\end{array} ,\mathrm{A}\
eq\Phi\right.\] (8) \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Method Step** & \multicolumn{4}{c}{**Detailed Description of Each Step**} \\ \hline Step 1 & Criteria number = 3 & Criterion 1 & Criterion 2 & Criterion 3 \\  & Names of criteria & Pressure resilience & State resilience & Response resilience \\  & Select the best & & Response resilience & \\  & Select the worst & & State resilience & \\  & Names of criteria & Pressure resilience & State resilience & Response resilience \\ Step 2 & Best to others & 2 & 3 & 1 \\ Step 3 & Others to the worst & 2 & 1 & 4 \\ Step 4 and Step 5 & Calculate node weights & 0.27 & 0.16 & 0.57 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Process for evaluating node weights using the BWM algorithm. \[K=\sum\
olimits_{X\cap Y=\Phi}m_{1}(X)m_{2}(Y)<1 \tag{9}\]  
where K represents conflicts between subset X and subset Y. For the fusion of resilience states across multiple nodes, combining the states of multiple nodes is possible as the node combination sequence does not affect the result in the DS evidence theory [50]. The process involves layering the resilience states of multiple nodes and fusing them in a hierarchical framework of resilience elements, as shown in Figure 8. The rule for fusing the resilience state of an element node into the resilience state of a factor node can be expressed as Equations (10) and (11), whereas the rule for fusing the resilience state of a factor node into the resilience state of a dimension node can be expressed as Equations (12) and (13). Finally, the rule for fusing the resilience state of a dimension node into the resilience state of the road operational resilience node can be expressed as Equations (14) and (15). \[m(e_{1}^{n})=S(e_{1}^{n})\lambda_{E_{1}^{n}} \tag{10}\]  
\[F_{i}=E_{i}^{1}\oplus E_{i}^{2}\oplus\ldots\oplus E_{i}^{n} \tag{11}\]  
where \(m(e_{i}^{n})\) represents the mass function of state for the n-th element node under the i-th factor. \(S(e_{i}^{n})\) evaluates the resilience status of the corresponding element node, while \(\lambda_{E_{i}^{n}}\) represents the weight of the corresponding element node. \(F_{i}\) denotes the resilience status of the i-th factor node, and \(E_{i}^{n}\) represents the resilience status of the n-th element node that influences \(F_{i}\). The combination of the resilience status of the n element nodes (\(E_{i}^{1}\)\(E_{i}^{2}\),..., \(E_{i}^{n}\)) is used to calculate the resilience status of the i-th factor node, \(F_{i}\). \[m(f_{i})=S(f_{i})\lambda_{F_{i}} \tag{12}\]  
\[D_{l}=F_{i}\oplus F_{2}\oplus\ldots\oplus F_{i} \tag{13}\]  
where \(m(f_{i})\) represents the mass function of the i-th factor node. \(S(f_{i})\) evaluates the resilience status of the corresponding factor node, while \(\lambda_{F_{i}}\) represents the weight of the corresponding factor node. The combination of the resilience status of the i factor nodes generates the resilience status of the l-th dimension node, \(D_{l}\).