## 4 Case Study
### Comparison with the Bayesian Network Method  
In order to make a comparison, we created a model using the Bayesian network-based method: we used the same structural model and identification framework employed for the evidential network to establish the conditional-probability-parameter table for capabilities in the space-navigation-and-positioning system of systems. Figure 4 shows the conditional-probability table for capability indicators defined in the capability-requirement-satisfaction model of the Bayesian network-based space-navigation-and-positioning system of systems. The difference between Figures 2 and 4 is that, in the event of cognitive uncertainty, the Bayesian network divides cognitive uncertainty into definite states. This is because Bayesian networks cannot handle cognitive uncertainties, so accurate probabilistic judgments are required before reasoning. This will inevitably lead to the loss of uncertain information. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Algorithm** & _m_**(c=H)** & _m_**(c=M)** & _m_**(c=L)** & _m_**(G)** \\ \hline Anti-jamming capability & 0.7211 & - & 0.2241 & 0.0548 \\ System survivability & 0.6588 & - & 0.1816 & 0.1596 \\ Security and confidentiality & 0.5008 & - & 0.3460 & 0.1533 \\ Navigation and positioning capability & 0.5647 & - & 0.2714 & 0.1639 \\ Space-navigation-and-positioning system capability & 0.3567 & 0.1656 & 0.1699 & 0.3077 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: The belief distribution of the requirement-satisfaction degree for each upper-layer capability. Figure 3: The belief distribution of the requirement-satisfaction degree of each upper-layer capability. Similarly, the determination of the prior probability of the underlying ability index also requires an accurate probability judgment. Cognitive uncertainty, should it occur, must be assigned to the definite states, as shown in Table 5. \begin{table}
\begin{tabular}{c c c} \hline
**Bottom Capability Indicators** & \(P_{0}\) **(c=H)** & \(P_{0}\) **(c=L)** \\ \hline Satellite survivability & 0.725 & 0.275 \\ Ground station survivability & 0.5 & 0.5 \\ Anti-compression capability & 0.571 & 0.429 \\ Anti-spoofing capability & 0.833 & 0.167 \\ Positioning accuracy & 0.658 & 0.342 \\ Speed accuracy & 0.7375 & 0.2625 \\ Timing accuracy & 0.543 & 0.447 \\ Encryption capability & 0.41 & 0.59 \\ Anti-virus capability & 0.59 & 0.41 \\ \hline \end{tabular}
\end{table} 
Table 5: The prior probability of bottom capability indicators. Figure 4: Conditional probability distribution (CPD) of spatial navigation and positioning capabilities. We used the Matlab BNT 1.0.7 toolbox in order to establish, via Figure 1, the structure of the Bayesian network. We then entered the conditional probability distribution (CPD) parameters and the prior probability of the underlying capability index, and obtained the marginal probability of each capability, as shown in Table 6.  
We compared Tables 4 and 6 to the data shown in Figure 5. We obtained _AJ, SS, SC, NP_ through the evidence-based method and _AJ'_, _SS'_, _SC'_, _NP'_ through the Bayesian-based method. The requirement-satisfaction degree with the highest value corresponds to the anti-jamming capability in the results obtained via the evidential network, while it corresponds to system survivability for results obtained through the Bayesian network. The methods--Bayesian and evidential--used to assess the degree of capability requirement satisfaction differed in mainly two aspects: parameter modeling and reasoning methods. The difference between parameter modeling in Bayesian networks and evidential networks is that the former requires an accurate probability judgment, while the latter does not. Moreover, the latter can both model cognitive uncertainty and handle the aspects that involve the researcher's ignorance on the subject. The difference between reasoning methods in Bayesian and evidential networks is that the former must make a fuzzy estimation of prior knowledge before initiating the reasoning process.