# Resilience Assessment for the Northern Sea Route Based on a Fuzzy Bayesian Network
## 3 Model Established for NSR Resilience Measurement
### Sensitivity Analysis  
Sensitivity analysis is one of the characteristic features of the application of BNs in identifying the most important independent variable(s) based on a particular dependent variable under a given set of conditions [77]. Herein, GeNle 2.3 software is applied to simulate the established BN model and investigate the extent to which the parent nodes differ from the target nodes.  
In the present study, the fuzzy ratio of variation (RoV) associated with the prior and posterior probabilities is calculated according to Equation (33) to evaluate the desired probability level of the contributing variables.  
\[RoV(X_{i})\ =\ \frac{\xi(X_{i})-\zeta(X_{i})}{\zeta(X_{i})} \tag{36}\]  
where \(X_{i}\) denotes the ith contributing factor and \(\zeta(X_{i})\) and \(\zeta(X_{i})\) represent the posterior and prior probabilities of \(X_{i}\), respectively. Actually, all the parent nodes in the Bayesian network can theoretically be analyzed.  
As discussed in Section 3.3, the NSR system resilience is mainly represented by the absorptive capacity, adaptive capacity, and restorative capacity. Therefore, in this section, we will set these individual capacities as the target nodes to investigate the corresponding effects of the contributing factors. Deductive reasoning is applied to update the probabilities of the contributing factors for the resilience related to the occurrence of the individual capacity (absorptive capacity, adaptive capacity, or restorative capacity), and then the value of the ratio of variation can be obtained by Equation (33). Finally, the results of the sensitivity analysis are illustrated in Figure 10.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Scenario** & **R1-2** & **R2-2** & **R3-1** & **Absorptive Capacity (\%)** & **Adaptive Capacity (\%)** & **Restorative Capacity (\%)** & **Resilience (\%)** \\ \hline Base & – & – & – & 93.4 & 98.0 & 88.2 & 78.5 \\
1 & _false_ & – & – & 89.2 (\(\downarrow\)) & 98.0 & 88.2 & 78.1 (\(\downarrow\)) \\
2 & _false_ & _false_ & – & 89.2 & 94.8 (\(\downarrow\)) & 88.2 & 77.8 (\(\downarrow\)) \\
3 & _false_ & _false_ & _false_ & 89.2 & 94.8 & 65.7 (\(\downarrow\)) & 75.9 (\(\downarrow\)) \\ \hline \hline \end{tabular} Note: \(\downarrow\) denotes a reduction in a certain variable value in the defined scenario compared with the value in the base case.  
\end{table}
Table 14: Different scenario sets for forward-propagation analysis.  
Figure 10: Sensitivity analysis for the absorptive capacity.  
Figure 10 shows the effects of individual contributing factors on the corresponding capacity. For the absorptive capacity, when the state is set as \"true\", it is obviously found that the contributing factor \"skilful emergency response\" (R1-5) has the most important influence on the desired absorptive capacity; moreover, the \"well-coordinated with tugs\" (R1-4) has the lowest impact on the improvement of the absorptive capacity. When the state of the adaptive capacity is set as \"true\", after updating the probabilities of parent nodes, we can obtain the values of RoV for the contributing factors, as shown in Figure 7, from (R2-1) to (R2-5). Similarly, the results indicate that the \"ice-breaking capacity\" has the highest influence on the expected adaptive capacity, and the \"information prediction service\" ranks second; however, the effect of the \"preparedness for arctic shipping\" on the adaptive capacity is almost negligible. For the restorative capacity, there is no evident difference among the three contributing factors, and the \"rescue and anti-pollution facility\" (R3-1) may be characterized as the most potential influence on the restorative capacity.