## 5 Verification and Application
### Application on Capability Demand Satisfaction Evaluation of SCS
Therefore, in order to address the uncertainties and conflicts, the reliability discounting factor is determined by employing the Jousselme distance of PHFBPAs, while the credibility discounting factor is determined using the entropy measure of PHFBPAs. According to Equation (37), the credibility discounting factors could be calculated as follows:  
\[\omega=[0.0833\ 0.0833\ 0.0833\ 0.0824\ 0.0814\ 0.0839\ 0.0836\ 0.0833 \ 0.0838\ 0.0847\ 0.0838\ 0.0833]^{\mathrm{T}}. \tag{51}\]  
Following Equation (42), the reliability discounting factors could be calculated as:  
\[v=[0.0834\ 0.0834\ 0.0834\ 0.0826\ 0.0816\ 0.0838\ 0.0837\ 0.0834\ 0.0836\ 0.0844\ 0.0836\ 0.0833]^{\mathrm{T}}. \tag{52}\]  
The credibility discounting factors and the reliability discounting factor are integrated to form the final weight to adjust the PHFBPAs of the evidence. Applying the combination rule of PHFET Equation (18) to fuse the modified evidence 11 times and use the score function of PHFBPA to obtain the final result as: \(score(m_{p1}(v_{1}))=0.8725,score(m_{p1}(v_{2}))=0.127,\)\(score(m_{p1}(v_{3}))=0.0005\). These scores indicate a high degree of satisfaction with the capability demand for scheme 1, suggesting that the Satellite Communication System (SCS) built according to this scheme possesses the necessary capabilities to successfully fulfill the mission. To facilitate a comparison between different schemes, assume that there are scheme 3 and scheme 4. Scheme 3 shares identical indicators with scheme 1, except for \(I_{6}=0.896\) and \(I_{7}=0.8267\). On the other hand, scheme 4 has identical indicators to scheme 1, except for \(I_{8}=0.335\). The fusion result for these four schemes are illustrated in Figure 4.  
Analyzing the satisfaction degrees of the four schemes reveals that scheme 1, scheme 3, and scheme 4 exhibit high levels of satisfaction, while scheme 2 demonstrates a moderate \begin{table}
\begin{tabular}{c c c c c c c c c c c c} \hline \hline
**Importance** & \(\mathbf{I_{1}}\) & \(\mathbf{I_{2}}\) & \(\mathbf{I_{3}}\) & \(\mathbf{I_{4}}\) & \(\mathbf{I_{5}}\) & \(\mathbf{I_{6}}\) & \(\mathbf{I_{7}}\) & \(\mathbf{I_{8}}\) & \(\mathbf{I_{9}}\) & \(\mathbf{I_{10}}\) & \(\mathbf{I_{11}}\) & \(\mathbf{I_{12}}\) \\ \hline Land communication & 0.6 & 0.8 & 0.8 & 0.7 & 0.6 & 0.75 & 0.5 & 0.8 & 0.8 & 0.8 & 0.8 & 0.8 & 0.6 \\ Maritime communication & 0.4 & 0.2 & 0.2 & 0.3 & 0.4 & 0.25 & 0.5 & 0.2 & 0.2 & 0.2 & 0.4 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Importance of mission. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**PHFBPAs** & \(m_{P}(\mathbf{v_{1}})\) & \(m_{P}(\mathbf{v_{2}})\) & \(m_{P}(\mathbf{v_{3}})\) \\ \hline \(m_{P1}\) & \{0.3794(0.6), 0.3415(0.4)\} & \{0.3309(0.6), 0.2978(0.4)\} & \{0.2898(0.6), 0.26070(0.4)\} \\ \(m_{P2}\) & \{0.4185(0.8), 0.3348(0.2)\} & \{0.3463(0.8), 0.2770(0.2)\} & \{0.2352(0.8), 0.18819(0.2)\} \\ \(m_{P3}\) & \{0.3512(0.8), 0.2809(0.2)\} & \{0.3474(0.8), 0.2779(0.2)\} & \{0.3015(0.8), 0.2412(0.2)\} \\ \(m_{P4}\) & \{0.3987(0.7), 0.2990(0.3)\} & \{0.3763(0.7), 0.2823(0.3)\} & \{0.2250(0.7), 0.1687(0.3)\} \\ \(m_{P5}\) & \{0.3357(0.6), 0.2350(0.4)\} & \{0.3344(0.6), 0.2341(0.4)\} & \{0.3299(0.6), 0.2310(0.4)\} \\ \(m_{P6}\) & \{0.3419(0.75),0.3248(0.25)\} & \{0.3354(0.75),0.3186(0.25)\} & \{0.3227(0.75),0.3066(0.25)\} \\ \(m_{P7}\) & \{0.4251(0.5), 0.4039(0.5)\} & \{0.3761(0.5), 0.3573(0.5)\} & \{0.1988(0.5), 0.1889(0.5)\} \\ \(m_{P8}\) & \{0.3865(0.8), 0.3092(0.2)\} & \{0.3956(0.8), 0.3165(0.2)\} & \{0.2179(0.8), 0.1743(0.2)\} \\ \(m_{P9}\) & \{0.3376(0.8), 0.3038(0.2)\} & \{0.3371(0.8), 0.3034(0.2)\} & \{0.3254(0.8), 0.2928(0.2)\} \\ \(m_{P10}\) & \{0.3419(0.8), 0.3761(0.2)\} & \{0.3403(0.8), 0.3744(0.2)\} & \{0.3177(0.8), 0.3495(0.2)\} \\ \(m_{P11}\) & \{0.3415(0.8), 0.3073(0.2)\} & \{0.3382(0.8), 0.3044(0.2)\} & \{0.3204(0.8), 0.2884(0.2)\} \\ \(m_{P12}\) & \{0.4654(0.6), 0.4189(0.4)\} & \{0.3199(0.6), 0.2879(0.4)\} & \{0.2147(0.8), 0.1933(0.4)\} \\ \hline \hline \end{tabular}
\end{table} 
Table 5: PHFBPAs of scheme 1.  
level.