## 5 Verification and Application
### Discussion  
To assess and validate the stability of the proposed algorithm, we conducted sensitivity analysis on the indicator weights and mission importance to examine their impact on the fusion result. We assigned different weights to the 12 indicators, denoted as \(\delta\) in Equation (43), creating three distinct weight sets, as shown in Table 6.  
Furthermore, in order to evaluate the effect of the basis for the possibility values in PHFBAs on the fusion result, Table 7 presents two more importance ratings for land and maritime communication missions in addition to those in Table 4.  
The experimental results, depicted in Figure 5, reveal that the priority order of satisfaction level remains consistent despite significant fluctuations in both indicator weights (Figure 5a) and mission importance (Figure 5b). These findings strongly support the stability and robustness of the introduced PHFET model under various weighting scenarios. \begin{table}
\begin{tabular}{c c c c c c c c c c c c c} \hline \hline
**Weight Set** & \(\mathbf{I_{1}}\) & \(\mathbf{I_{2}}\) & \(\mathbf{I_{3}}\) & \(\mathbf{I_{4}}\) & \(\mathbf{I_{5}}\) & \(\mathbf{I_{6}}\) & \(\mathbf{I_{7}}\) & \(\mathbf{I_{8}}\) & \(\mathbf{I_{9}}\) & \(\mathbf{I_{10}}\) & \(\mathbf{I_{11}}\) & \(\mathbf{I_{12}}\) \\ \hline
1 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 & 1/12 \\
2 & 0.151 & 0.032 & 0.312 & 0.012 & 0.144 & 0.132 & 0.035 & 0.067 & 0.005 & 0.014 & 0.081 & 0.015 \\
3 & 0.017 & 0.051 & 0.081 & 0.036 & 0.123 & 0.092 & 0.094 & 0.225 & 0.068 & 0.097 & 0.106 & 0.01 \\ \hline \hline \end{tabular}
\end{table} 
Table 6: Weight sets of indicators. Figure 4: Satisfaction degrees of different schemes. These results reaffirm the effectiveness and reliability of the proposed algorithm for the decision-making processes. The algorithm's ability to maintain consistent performance across different weight configurations enhances its practical applicability. Decision-makers can confidently use this model without concerns about unpredictable or inconsistent outcomes due to variations in experts' weights. Additionally, the stability analysis provides a solid foundation for future research and potential refinements of the algorithm. Several traditional methods have been adopted for comparison, including [PERSON]'s method [39], referred to as '[PERSON]'; [PERSON]'s method [40], referred to as '[PERSON]'; [PERSON] et al. 's method [41], referred to as '[PERSON]'; [PERSON]'s method [42], referred to as '[PERSON]'; and [PERSON]'s method [36], referred to as '[PERSON]'. To verify the effectiveness of the proposed discounting factors in eliminating uncertainty and conflicting evidence, several variants of the PHFET method are utilized. The PHFET method without the discounting of evidence is denoted as 'PHFET', while the versions with credibility discounting factor and reliability discounting factor are denoted as 'PHFET-1' and 'PHFET-2', respectively. Furthermore, the combination of both discounting factors is denoted as 'PHFET-12'. According to the distance-based generation method proposed in the previous section, PHFBPs of scheme 1 were obtained. Furthermore, to facilitate comparison with other methods, the adjustment parameter \(\alpha\) in Equation (31) takes the values of 1 and 1, with a probability of 0.5 for each value. The final fusion results of the evidence from all indicators are depicted in Figure 6.  
Figure 5: Stability analysis. (**a**) Fusion results with different indicator weights; (**b**) fusion results with different mission importance. Figure 6: Fusion results of different methods. As can be seen from Figure 6, most of the methods allocate the largest belief mass to \(v_{1}\), indicating sufficient capabilities to carry out the mission as intended, except for [PERSON]'s method and [PERSON] et al. 's method. These two methods allocate most of the belief mass to an unknown space \(V\), indicating that they cannot provide a specific satisfaction level.