# Resilience Assessment for the Northern Sea Route Based on a Fuzzy Bayesian Network
## 3 Model Established for NSR Resilience Measurement
### Resilience Quantification  
Many studies have been performed to evaluate the resilience of a specified system, and different models have been proposed to quantify system resilience. In the present study, the model developed by [28] is utilized to measure the resilience of Arctic Northeast Route security. Specifically, resilience is defined as the ratio of the recovery capacity to the loss capacity of the system, which can be expressed by:  
\[R~{}=~{}\frac{recovery}{loss} \tag{35}\]  
In the present study, the loss capacity variable of the system is conditioned based on three variables, namely, the probability of disruption occurrence (PDO), the absorptive capacity, and the actual security capacity (ASC). In practice, the loss capacity is greatly dependent on the degree to which the absorptive capacity is capable of withstanding the system shocks caused by disruptions; that is, the probability of the absorptive capacity being in a true state. If the state of the absorptive capacity is true (the probability is 100%), then the loss capacity will be zero. The actual security capacity is set as a constant in the present study because both the absorptive capacity and recovery capacity are associated with the actual security capacity in the expression of the resilience measurement. Therefore, the loss capacity can be obtained according to Table 12.  
The recovery capacity of the system is dependent on the effectiveness of the post-disruption strategy (the combination of the adaptive capacity and restorative capacity) and the degree of the Loss Capacity (LC). If the post-disruption strategy is fully effective, that is, the state of the post-disruption strategy is true, the security system will recover 85% of the loss capacity; otherwise, the value will be zero. Therefore, the recovery capacity can be calculated according to Table 13.  
\begin{table}
\begin{tabular}{c c c c c} \hline \hline \multicolumn{6}{c}{**Expert Judgement**} \\ \hline \(Y\gets X_{1}\): & M & H & H & M & H \\ \(Y\gets X_{2}\): & M & L & L & M & VH \\ \(Y\gets X_{3}\): & VH & H & M & H & H \\ \multicolumn{6}{c}{Aggregation of expert judgement (the same method as adopted for the aggregated value in Table 10)} \\ \hline \multicolumn{6}{c}{\(P(Y\gets X_{1})=0.6528~{}P(Y\gets X_{2})=0.4615~{}P(Y\gets X_{3})=0.7225\)} \\ \multicolumn{6}{c}{Conditional probability calculation by the Noisy-OR model} \\ \hline \multicolumn{6}{c}{\(P(Y\gets X_{1},~{}X_{2})=1-(1-P(Y\gets X_{1}))*(1-P(Y\gets X_{2}))=0.8130\)} \\ \(P(Y\gets X_{1},~{}X_{3})=1-(1-P(Y\gets X_{1}))*(1-P(Y\gets X_{3}))=0.9037\) \\ \(P(Y\gets X_{2},~{}X_{3})=1-(1-P(Y\gets X_{2}))*(1-P(Y\gets X_{3}))=0.8506\) \\ \multicolumn{6}{c}{\(\ldots\ldots\)} \\ \multicolumn{6}{c}{Conditional probability table for the node “nav. Service out of order” (\(Y\))} \\ \hline \(P(Y\gets X_{1},~{}\overline{X_{2}},~{}\overline{X_{3}})=0.6528~{}P(Y \gets X_{1},~{}X_{2},~{}\overline{X_{3}})=0.8130\) \\ \(P(Y\gets X_{2},~{}\overline{X_{1}},~{}\overline{X_{3}})=0.4615~{}P(Y \gets X_{1},~{}\overline{X_{2}},~{}X_{3})=0.9037\) \\ \(P(Y\gets X_{3},~{}\overline{X_{1}},~{}\overline{X_{2}})=0.7225~{}P(Y \leftarrow\overline{X_{1}},X_{2},~{}X_{3})=0.8506\) \\ \(P(Y\gets X_{1},~{}\overline{X_{2}},~{}\overline{X_{3}})=0.0519~{}P(Y \gets X_{1},X_{2},~{}X_{3})=0.9481\) \\ \hline \hline \end{tabular}
\end{table}
Table 11: Calculation process for the conditional probabilities of the node “nav. service out of order”.  
\begin{table}
\begin{tabular}{c c c} \hline \hline
**State of the Absorptive Capacity** & **True** & **False** \\ \hline Expression & PDO \(\times\) ASC & 0 \\ \hline \hline \end{tabular}
\end{table}
Table 12: Conditional calculation of the loss capacity.