## 4 Case Study
### Comparisons  
In this section, to validate the effectiveness of the proposed QFD method, it is compared and analyzed against traditional QFD, fuzzy QFD [38], and an extended linguistic QFD method based on discrete numbers [39] on the same issue of market segmentation assessment. Table 14 displays the results of the ranking results of ECs obtained through these four methods. The implementation details of the traditional QFD method are omitted here. Next, we will only describe the application processes of the fuzzy QFD and the linguistic QFD methods. For the Fuzzy QFD method, a panel of five decision-makers is assembled to analyze the correlation between CRs and ECs, and the used linguistic rating set is U = {VL, L, M, H, VH}, where VL = Very Low = (0.0, 0.1, 0.2), L = Low = (0.1, 0.3, 0.5), M = Medium = (0.4, 0.5, 0.7), \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & \(C_{5}\) \\ \hline \(A_{1}\) & [0.005, 0.008] & [0.004, 0.005] & [0.005, 0.008] & [0.006, 0.01] & [0.001, 0.002] \\ \(A_{2}\) & [0.003, 0.004] & [0.004, 0.005] & [0.006, 0.008] & [0.006, 0.01] & [0.000, 0.001] \\ \(A_{3}\) & [0.003, 0.004] & [0.004, 0.005] & [0.006, 0.008] & [0.008, 0.012] & [0.001, 0.002] \\ \(A_{4}\) & [0.003, 0.005] & [0.004, 0.005] & [0.006, 0.008] & [0.006, 0.008] & [0.001, 0.002] \\ \hline \hline \end{tabular}
\end{table} 
Table 12: Weighted standardized decision matrix. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(D(A_{i}A^{*})\) & \(D(A_{i}A^{-})\) & \(S_{i}\) & **Ranking** \\ \hline \(A_{1}\) & 0.0021 & 0.0036 & 0.6296 & 1 \\ \(A_{2}\) & 0.0039 & 0.0016 & 0.2899 & 3 \\ \(A_{3}\) & 0.0032 & 0.0034 & 0.5175 & 2 \\ \(A_{4}\) & 0.0041 & 0.0014 & 0.2582 & 4 \\ \hline \hline \end{tabular}
\end{table} 
Table 13: Relative closeness and ranking results of ECs. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline  & \(C_{1}\) & \(C_{2}\) & \(C_{3}\) & \(C_{4}\) & \(C_{5}\) \\ \hline \(A_{1}\) & [0.023, 0.034] & [0.029, 0.034] & [0.023, 0.034] & [0.017, 0.029] & [0.023, 0.029] \\ \(A_{2}\) & [0.011, 0.017] & [0.029, 0.034] & [0.029, 0.034] & [0.017, 0.029] & [0.006, 0.017] \\ \(A_{3}\) & [0.011, 0.017] & [0.029, 0.034] & [0.029, 0H = High = (0.5, 0.7, 0.9), and VH = Very High = (0.8, 0.9, 1.0). The fuzzy evaluations provided by the experts are shown in Table 15. After converting them into fuzzy numbers, the fuzzy values for the weights of each \"HOW\" attribute are obtained by averaging the total weighted correlation scores with the total weights of \"WHAT\", and then they are ranked based on the importance weights of \"HOWs\". For the linguistic QFD method, a decision-making team consisting of three members is established. The three decision-makers compared the four alternatives (\(x_{i}(i=1,2,3,4)\)) using the linguistic term set T, where T = {\(t_{1}\) = extremely poor, \(t_{2}\) = very poor, \(t_{3}\) = poor, \(t_{4}\) = slightly poor, \(t_{5}\) = fair, \(t_{6}\) = slightly good, \(t_{7}\) = good, \(t_{8}\) = very good, \(t_{9}\) = extremely good), and constructed linguistic preference relations \(R_{k}(k=1,2,3)\), respectively, as shown in Tables 16-18. To determine the optimal alternative, two new aggregation operators are developed, which can be used to aggregate preference information in the form of linguistic variables. Based on the LGA and LHGA operators, the preference degrees of each alternative relative to the others can be obtained, facilitating the ranking process.