# Resilience Assessment for the Northern Sea Route Based on a Fuzzy Bayesian Network
## 3 Model Established for NSR Resilience Measurement
### Resilience Measurement Using the Fuzzy Bayesian Network
#### 3.4.3 Calculation of the Condition Probability Table for the Network  
To obtain the conditional probability table for the nodes with multiple parents, the leaky Noisy-OR function is applied considering that the states of child nodes may be false even if all the parent nodes are true. Based on the calculated connection probability, \(P_{l}\), for each parent node, the Leaky Noisy-OR function can be expressed as:  
\[NoisyOR(P_{1},\ X_{1},P_{2},\ X_{2},\ldots,P_{n},\ X_{n},l) \tag{33}\]  
where \(l\) represents the leaky factor, indicating the degree to which the missing causal factors contribute to a consequence being true. Generally, the leaky factor is a nonzero probability, even if all the causal factors are false. Therefore, the leaky factor represents a probability that implies that the child node will be true if the parent nodes are false, as expressed below.  
\[l\ =\ P(\ Y\ =\ true|X_{1}\ =\ false,X_{2}\ =\ false,\ldots,X_{n}\ =\ false)\
eq 0 \tag{34}\]  
In the present study, five experts with attributes described in Section 3.4.1 were employed to give their judgements regarding the conditional probabilities of nodes with multiple parent nodes in the form of linguistic expressions. The expert insights were further processed based on the fuzzy methodology proposed in Section 2.1, after which the conditional probabilities for child nodes can be expressed by the Noisy-OR function as follows:  
\(P(\mathit{Nav.\ service\ out\ of\ order})\ =\ Noisy-OR([D1-1],0.6277,[D1-2],0.5870,[D1-3],0.3626,0.05)\)  
\(P(\mathit{equipment\ failure})\ =\ Noisy-OR([D2-1],0.49,[D2-2],0.26,[D2-3],0.80,[D2-4],0.58,0.032)\)  
\(P(\mathit{severe\ nautical\ env.})\ =\ \\ NoisyOR([D3-1],0.43,[D3-2],0.38,[D3-3],0.87,[D3-4],0.61,[D3-5],0.39,0.011)\)  
\(P(\mathit{other\ disruptions})\ =\ NoisyOR([D4-1],0.24,[D4-2],0.57,[D4-3],0.33,0.218)\)  
\(P(\mathit{restorative\ capacity})\ =\ NoisyOR([R3-1],0.84,[R3-2],0.68,[R3-3],0.69,0.016)\)  
\(P(\mathit{adaptive\ capacity})\ =\ \\ NoisyOR([R2-1],0.94,[R2-2],0.88,[R2-3],0.17,[R2-4],0.71,[R2-5],0.92,0.02)\)  
\(P(\mathit{defentive\ capacity})\ =\ NoisyOR([R1-1],0.41,[R1-3],0.57,[R1-5],0.21,[R1-6],0.96,0.009)\)  
\(P(\mathit{emergency\ capacity})\ =\ NoisyOR([R1-2],0.90,[R1-7],0.89,[R1-8],0.67,0.04)\)  
The conditional probability table for the proposed Bayesian network can be induced by combining the Noisy-OR function of child nodes with Equation (26). To concisely represent the computing process for the CPT, the node \"service out of order\" (\(\gamma\)) with three  
\begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Item** & **Aggregated Value** & **Item** & **Aggregated Value** & **Item** & **Aggregated Value** \\ \hline D1-1 & 0.6528 & D3-4 & 0.5325 & R1-6 & 0.67 \\ D1-2 & 0.4615 & D3-5 & 0.5445 & R1-7 & 0.6198 \\ D1-3 & 0.7225 & D4-1 & 0.4355 & R2-1 & 0.5445 \\ D2-1 & 0.7084 & D4-2 & 0.7807 & R2-2 & 0.7085 \\ D2-2 & 0.6036 & D4-3 & 0.6438 & R2-3 & 0.5021 \\ D2-3 & 0.7338 & R1-1 & 0.5887 & R2-4 & 0.6635 \\ D2-4 & 0.7138 & R1-2 & 0.8142 & R2-5 & 0.8594 \\ D3-1 & 0.6468 & R1-3 & 0.4994 & R3-1 & 0.7897 \\ D3-2 & 0.7818 & R1-4 & 0.5079 & R3-2 & 0.6083 \\ D3-3 & 0.6641 & R1-5 & 0.7892 & R3-3 & 0.6097 \\ \hline \hline \end{tabular}
\end{table}
Table 10: Aggregation results for each Boolean variable based on expert elicitation.  
parent nodes (\(X_{1},~{}X_{2},~{}X_{3}\)) was taken as an example, and the exhaustive information is given in Table 11.