## 5 Conclusions  
In the supply chain, each company is dependent upon others in the line; therefore, supply chain members can work together to reduce operational costs and improve productivity and performance. However, a key question is how to measure and select the most suitable supplier. Generally speaking, managers often rely on past personal experience or subjective assertions, or adopt the Likert scale to evaluate, compare, and rank the performance of suppliers. However, these approaches have some \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Manager** & **Criterion** & **C1 (Cost)** & **C2 (Cost)** & **C3 (Benefit)** & **C4 (Benefit)** & **Crisp Value** \\ \hline Manager 1 & N (5) & VL (9) & G (7) & VG (9) & 86.4 \\ Manager 2 & L (7) & VL (9) & N (5) & G (7) & 70 \\ Manager 3 & VL (9) & N (5) & G (7) & N (5) & 70 \\ Manager 4 & L (7) & N (5) & VG (9) & G (7) & 70 \\ Manager 5 & L (7) & L (7) & G (7) & G (7) & 86.7 \\ Manager 6 & VL (9) & N (5) & N (5) & VG (9) & 70 \\  & & \(\overline{X}=75.5\) & & & \\  & & \(s=8.5\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 8: Results of Supplier 2. \begin{table}
\begin{tabular}{c c c c c c} \hline \hline
**Manager** & **Criterion** & **C1 (Cost)** & **C2 (Cost)** & **C3 (Benefit)** & **C4 (Benefit)** & **Crisp Value** \\ \hline Manager 1 & VL (9) & VL (9) & G (9) & VG (9) & 96.7 \\ Manager 2 & N (5) & L (7) & N (5) & N (5) & 50 \\ Manager 3 & L (7) & L (7) & N (5) & VG (9) & 70 \\ Manager 4 & VL (9) & VL (9) & G (9) & VG (9) & 96.7 \\ Manager 5 & L (7) & N (5) & N (5) & VG (9) & 70 \\ Manager 6 & VL (9) & VL (9) & N (5) & N (5) & 70 \\  & & \(\overline{X}=75.5\) & & & \\  & & \(s=18.11\) & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 9: Results of Supplier 3.  
disadvantages. They tend to neglect stakeholders' preferences as well as cognitive differences among evaluators. Furthermore, when the opinions of multiple decision-makers are combined, issues such as cognitive differences, fuzzy linguistics, and uncertainty are common. To fill these gaps, this study presents a supplier performance index \(S_{PL}\), and derives the estimator \(\hat{S}_{PL}\) and its PDF. Subsequently, the Fuzzy Logic Toolbox from MATLAB 2017b is used to obtain crisp values in a fuzzy environment. To demonstrate the efficacy of the proposed method, this study uses a real-world case study for supplier selection of high-voltage power film capacitors for a gas turbine factory. Finally, we compared the proposed method with existing methods. This paper has two important managerial implications. First, the proposed approach provides guidelines for managers, assisting not only with the problem of cognitive preferences and differences, but also in the solution of the supplier selection problem in the mechanical engineering industry. Second, companies can relay the results of the proposed method to unsuccessful suppliers to give them an understanding of their shortcomings and help them improve their performance, which will enhance the competitiveness of the supply chain and create win-win situations for both parties. The major contributions of this study are six-fold: (i) when the opinions of multiple decision-makers are combined, the proposed method can effectively resolve issues such as cognitive differences, fuzzy linguistics, and uncertainty in the supplier selection process; (ii) the proposed method enables analysis data to be easily obtained from investigations of buyers and suppliers; (iii) the proposed method can serve as an effective tool with which companies can manage and control the quality of the supplier selection process; (iv) the proposed method can be used by supply chain members to evaluate and determine suitable suppliers in a fuzzy environment; (v) the proposed method could be profitably extended to the process of supplier selection in other industries; and (vi) evaluation data that follow a non-normal skewed distribution could also be considered for supplier selection [59]. Conceptualization, C.-M.Y. and C.-H.H. ; Data curation, T.-H.H. and C.-H.H.