## 4 Numerical Example and Comparative Analysis
### Comparative Analysis  
Then, we compare our proposed operators with single valued neutrosophic weighted averaging (SVNWA) operator and single valued neutrosophic weighted geometric (SVNWG) operator [35]. The comparative results are depicted in Table 6.  
\begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(R\) & \(S(\mathbf{O_{1}})\) & \(S(\mathbf{O_{2}})\) & \(S(\mathbf{O_{3}})\) & \(S(\mathbf{O_{4}})\) & \(S(\mathbf{O_{5}})\) & **Order** \\ \hline (1,1,1,1) & 0.5511 & 0.6381 & 0.5711 & 0.5944 & 0.5127 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (2,2,2,2) & 0.4108 & 0.4996 & 0.4227 & 0.4517 & 0.3726 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (3,3,3,3) & 0.3619 & 0.4291 & 0.3670 & 0.3985 & 0.3208 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (4,4,4,4) & 0.3385 & 0.3920 & 0.3405 & 0.3728 & 0.2962 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (5,5,5,5) & 0.3245 & 0.3702 & 0.3252 & 0.3572 & 0.2817 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (6,6,6,6) & 0.3149 & 0.3562 & 0.3153 & 0.3462 & 0.2716 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (7,7,7,7) & 0.3076 & 0.3467 & 0.3084 & 0.3377 & 0.2641 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (8,8,8,8) & 0.3018 & 0.3398 & 0.3032 & 0.3308 & 0.2582 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (9,9,9,9) & 0.2978 & 0.3347 & 0.3002 & 0.3251 & 0.2531 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (10,10,10,10) & 0.4150 & 0.3307 & 0.4182 & 0.3203 & 0.2505 & \(\text{O}_{3}>\text{O}_{1}>\text{O}_{2}>\text{O}_{4}>\text{O}_{5}\) \\ \hline \hline \end{tabular}
\end{table}
Table 4: Order for different parameters of DGSVNNWGBM.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **DGSVNNWBM** & **DGSVNNWGBM** \\ \hline O\({}_{1}\) & 0.5552 & 0.5511 \\ O\({}_{2}\) & 0.6395 & 0.6381 \\ O\({}_{3}\) & 0.5747 & 0.5711 \\ O\({}_{4}\) & 0.5969 & 0.5944 \\ O\({}_{5}\) & 0.5168 & 0.5127 \\ \hline \hline \end{tabular}
\end{table}
Table 2: The scores of the strategic suppliers.  
\begin{table}
\begin{tabular}{c c} \hline \hline  & **DGSVNNWBM** & **DGSVNNWGBM** \\ \hline O\({}_{1}\) & 0.5552 & 0.5511 \\ O\({}_{2}\) & 0.6395 & 0.6381 \\ O\({}_{3}\) & 0.5747 & 0.5711 \\ O\({}_{4}\) & 0.5969 & 0.5944 \\ O\({}_{5}\) & 0.5168 & 0.5127 \\ \hline \hline \end{tabular}
\end{table}
Table 3: Order of the strategic suppliers.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline \(R\) & \(S(\mathbf{O_{1}})\) & \(S(\mathbf{O_{2}})\) & \(S(\mathbf{O_{3}})\) & \(S(\mathbf{O_{4}})\) & \(S(\mathbf{O_{5}})\) & **Order** \\ \hline (1,1,1,1) & 0.5511 & 0.6381 & 0.5711 & 0.5944 & 0.5127 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (2,2,2,2) & 0.4108 & 0.4996 & 0.4227 & 0.4517 & 0.3726 & \(\text{O}_{2}>\text{O}_{4}>\text{O}_{3}>\text{O}_{1}>\text{O}_{5}\) \\ (3,3,3,3) & 0.3619 & 0.4291 & 0.3670 From above, we can we get the same results to show the effectiveness and practicality of the proposed operators. However, the existing aggregation operators, such as SVNWA operator and SVNWG operators, don't take into account the relationship between aggregated arguments, and thus cannot eliminate the influence of unfair arguments on decision results. Our proposed DGSVNNWBM and DGSVNNWGBM operators consider the information about the relationship among multiple arguments being aggregated.