## 8 Comparative Analysis  
This section of the paper provides a comparative analysis to ensure the stability of the suggested work. Before proceeding, it is recommended that you review Remark 1 in Section 3 and Table 1 to comprehend the superiority of the provided work. For example, if we set \(p=q=r=2\), we can derive the BT-SF TOPSIS technique. In addition, if we remove the neutrality degree membership and set \(p=r\), the q-ROF TOPSIS technique can be achieved. For additional study, we consider the numerical data in Tables 9, 11 and 12. We used our proposed approaches along with existing ones to the data supplied by the decision expert. The relative closeness of the alternatives suggests that \(\vec{v}_{3}\) is the optimum alternative for all the previously described techniques, except in q-ROF TOPSIS, where \(q=3,5,15\), \(\vec{v}_{4}\) is optimal, whereas either \(\vec{v}_{1}\) or \(\vec{v}_{2}\) is ranked last; see Figures 4, 6 and 7. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline \(\mathbf{B_{pqr}SFWA}\) & \(\boldsymbol{scor(\vec{\tau}_{1})}\) & \(\boldsymbol{scor(\vec{\tau}_{2})}\) & \(\boldsymbol{scor(\vec{\tau}_{3})}\) & \(\boldsymbol{scor(\vec{\tau}_{4})}\) & **Ranking Results** \\ \hline \(p=3,q=4,r=5\) & 0.605 & 0.6205 & 0.5996 & 0.6793 & \(\vec{v}_{4}\succ\vec{v}_{2}\succ\vec{v}_{1}\succ\vec{\tau}_{3}\) \\ \(p=5,q=4,r=3\) & 0.5494 &  
For the second method, Remark 1 in Section 3 justifies that different existing aggregation operators (in the contexts of IFSs, PyFSs, FFSs, q-ROFSs, mn-ROFSs, PFSs, PFS, SFSs, T-SFSs, pqr-FSs, BIFSs, BPyFSs, FBFSs, Bq-ROFSs, Bmn-ROFSs, BPFSs, SBFSs, and BT-SFSs) can be deduced from the Bpqr-SFWA operator. The aggregated results presented in Tables 10 and 13-18 suggest that \(\check{\tau}_{4}\) is the best alternative to be selected in almost all the operators except in the T-SF-weighted average (T-SFWA) and BTSF-weighted average (BTSFWA) operators for \(q=1\), where \(\check{\tau}_{2}\) is the best. The good news is that the score values generated by the proposed operators for various values of \(p,q\), and \(r\) demonstrate that the results almost match their findings, implying the proposed work's stability. Figures 5 and 8-13 show how the prospective operators' score values compare to those of existing  
Figure 8: Ranking results of pqr-SFWA operators for different values of p,q,r. \begin{table}
\begin{tabular}{c c c c c c} \hline
**pqr-SFWA** & \(\mathit{scor}(\pi_{1})\) & \(\mathit{scor}(\pi_{2})\) & \(\mathit{scor}(\pi_{3})\) & \(\mathit{scor}(\pi_{4})\) & **Ranking Results** \\ \hline \(p=3,q=4,r=5\) & 0.5737 & 0.5863 & 0.5738 & 0.6372 & \(\pi_{4}\succ\pi_{2}\succ\pi_{3}\succ\pi_{1}\) \\ \(p=5,q=4,r=3\) & 0.5307 & 0.5373 & 0.507 & 0.5833 & \(\pi_{4}\succ\pi_{2}\succ\pi_{1}\succ\pi_{3}\) \\ \(p=2,q=4,r=6\) & 0.6149 & 0.631 & 0.6187 & 0.6809 & \(\pi_{4}\succ\pi_{2}\succ\pi_{3}\succ\pi_{1}\) \\ \(p=3,q=5,r=7\) & 0.5737 & 0.5865 & 0.5774 & 0.6373 & \(\pi_{4}\succ\pi_{2}\succ\pi_{3}\succ\pi_{1}\) \\ \(p=7,q=5,r=3\) & 0.5131 & 0.5167 & 0.4884 & 0.5529 & \(\pi_{4}\succ\pi_{2}\succ\pi_{1}\succ\pi_{3}\) \\ \hline \end{tabular}
\end{table} 
Table 13: pqr-SFWA Ranking Results. Figure 7: BT-SFS TOPSIS ranking results, for q = 1,2,3,5.