# A New Flexible Method for Solving Multi-Expert Multi-Criterion Decision-Making Problems
## 4 Numerical Verification and Comparison
### Solution from the Proposed New Group DM Approach  
The proposed new group DM approach integrates an induced LOWGA operator and a HFLTS to increase the assessment ability of group decision-making problems. According to the judgments of committee members, a hierarchical structure of CNC machine tool selection was established. The criterion weights and criterion rating values for all alternatives were then identified, as shown in Figure 2 and Tables 1 and 2 (Steps 1 and 2). In this step, all incomplete information is supplemented by averaging all existing complete information. This results in complete criterion weights and criterion rating values for the five alternatives, as shown in Tables 3 and 4. Step 4. Defuzzify the hesitant values of assessment criterion data. Equation (6) was used to obtain the defuzzified results shown in Tables 3 and 4. Step 5. Use the fuzzy linguistic quantifier to calculate weighting vectors. According to Equations (7) and (8), we used the fuzzy linguistic quantifier \"Most\" to obtain weighting vectors. Step 6. Calculate the overall \(z_{i}\) values of alternatives \(x_{i}\), respectively [43]. According to Table 4, we defuzzified the hesitant values of the assessment criterion data for CNC machine tool selection, then aggregated the expert provided information, as shown in Table 5. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Decision-**} & \multirow{2}{*}{**Alternatives**} & \multicolumn{6}{c}{**Criteria**} \\ \cline{3-8}  & & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** \\ \hline \multirow{4}{*}{\(D1\)} & \(A1\) & 0.571 & 1 & 0.571 & 0.286 & 0.429 & 0.714 \\  & \(A2\) & 0.857 & 1 & 0.429 & 1 & 0.714 & 0.857 \\  & \(A3\) & 1 & 0.429 & 0.857 & 0.571 & 0.429 & 0.857 \\  & \(A4\) & 0.857 & 0.571 & 0.714 & 0.714 & 0.857 & 0.857 \\  & \(A5\) & 1 & 0.857 & 1 & 0.714 & 0.714 & 0.857 \\ \hline \multirow{4}{*}{\(D2\)} & \(A1\) & 0.857 & 0.571 & 0.762 & 0.571 & 0.667 & 0.857 \\  & \(A2\) & 0.857 & 0.857 & 0.762 & 0.714 & 0.714 & [0.857, 1] \\  & \(A3\) & 1 & 0.429 & 0.714 & 0.571 & 0.571 & 0.857 \\  & \(A4\) & 0.857 & 0.429 & 0.714 & 0.857 & 0.714 & [0.714, \\  & \(A5\) & 0.857 & 1 & 0.857 & 1 & 0.667 & [0.857] \\ \hline \multirow{4}{*}{\(D3\)} & \(A1\) & 0.714 & 1 & 0.714 & 0.571 & 0.571 & 0.857 \\  & \(A2\) & 1 & 0.857 & 0.429 & 0.857 & 0.714 & 0.857 \\  & \(A3\) & 1 & 0.714 & 1 & 0.429 & 0.571 & 0.857 \\  & \(A4\) & 1 & 0.571 & 0.714 & 0.714 & 0.571 & 0.714 \\  & \(A5\) & 0.857 & 1 & 1 & 0.714 & 0.571 & 0.857 \\ \hline \multirow{4}{*}{\(D4\)} & \(A1\) & [0.429, 0.571] & 0.857 & 0.571 & 0.571 & 0.429 & 0.857 \\  & \(A2\) & 0.857 & 1 & 0.571 & 0.857 & 1 & 0.714 \\ \cline{1-1}  & \(A3\) & 1 & 0.429 & 0.714 & [0.429, 0.571] & 0.571 & 0.714 \\ \cline{1-1}  & \(A4\) & 0.857 & 0.571 & 0.714 & 0.857 & 0.714 & 1 \\ \cline{1-1}  & \(A5\) & [0.857, 1] & 0.857 & 1 & 0.857 & [0.571, 0.714] & 0.857 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Complete information of criterion rating values for alternatives. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Alternatives**} & \multicolumn{6}{c}{**Criterion**} \\ \cline{2-7}  & **C1** & **C2** & **C3** & **C4** & **C5** & **C6** \\ \hline \(A1\) & 0.661 & 0.857 & 0.655 & 0.500 & 0.524 & 0.821 \\ \(A2\) & 0.893 & 0.929 & 0.548 & 0.857 & 0.786 & 0.839 \\ \(A3\) & 1.000 & 0.500 & 0.821 & 0.518 & 0.536 According to Table 5 and Equation (5),  
\[