## 4 Case Study  
In order to illustrate how the proposed method can be utilized in practical applications, we considered a manufacturer of gas turbine engines in Taiwan--Company A. It is one of the few professional gas turbine engine manufacturers in the country. The gas turbine engines are used for power transmission in airplanes, large ships, and automotive vehicles. In the manufacturing of gas turbine engines, high-voltage power film capacitors (see Figure 6) play a crucial role. Capacitors of poor quality can cause continued heat accumulation, rising temperatures, and low heat dissipation efficiency, which may lead to malfunctions and a shortened service life for gas turbine engines. These potential malfunctions can be dangerous, threatening life and property. Moreover, with the technological advances and innovations in materials made in recent years, Company A has developed a series of next-generation gas turbine engines that can achieve the same performance as previous gas turbine engines using only half of the specifications and materials. To increase the market share of their existing products in the current market and enable their new products to penetrate the market, Company A must employ an effective approach to evaluate the product performance of high-voltage power film capacitor suppliers in manufacturing high-quality gas turbine engines. The proposed method was used to achieve these ends. \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline \(n\) & \(b_{n}\) & \(n\) & \(b_{n}\) & \(n\) & \(b_{n}\) & \(n\) & \(b_{n}\) \\ \hline
3 & 0.580 & 10 & 0.914 & 17 & 0.952 & 24 & 0.967 \\
4 & 0.725 & 11 & 0.923 & 18 & 0.955 & 25 & 0.968 \\
5 & 0.798 & 12 & 0.930 & 19 & 0.958 & 26 & 0.970 \\
6 & 0.841 & 13 & 0.936 & 20 & 0.960 & 27 & 0.971 \\
7 & 0.869 & 14 & 0.941 & 21 & 0.962 & 28 & 0.972 \\
8 & 0.888 & 15 & 0.945 & 22 & 0.964 & 29 & 0.973 \\
9 & 0.903 & 16 & 0.949 & 23 & 0.965 & 30 & 0.974 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Values of \(b_{n}\) with varying \(n\). \begin{table}
\begin{tabular}{c c c} \hline \hline
**Score** & **Performance** & **Result** \\ \hline Crisp value \(>75\) & Excellent & Buyers will order again, and suppliers will not change their model. \\ \(60\leq\text{Crisp value}\leq 75\) & Good & Buyers will order again, but suppliers should prevent their \\  & & & product quality from falling. \\ \(30<\text{Crisp value}<60\) & Fair & Buyers will decline to order again unless the buyer is willing to \\  & & & reduce the level of demand. \\ Crisp value \(\leq 30\) & Poor & Buyers will decline to order, and suppliers should improve \\  & & & product quality. \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Supplier performance guide. Following consultation with experts and Company A's managers, and with reference to Table 1, Company A decided to adopt the following four criteria to evaluate the capability levels of three suppliers of high voltage power film capacitors: delivery (C1), price (C2), quality (C3), and service (C4). Among these four criteria, C1 and C2 are cost criteria and the remaining are benefit criteria. The five-point Likert scale questionnaire was adopted for the assessment of these suppliers by six managers (decision-makers). The six managers that were chosen all had more than 10 years' experience in executive positions. Table 6 presents the positions and experience of these six managers. Since the linguistic information provided by the managers represents qualitative data, fuzzy theory is used to convert each linguistic variable into a fuzzy number (quantification). For example, the linguistic labels {Very High; High; Normal; Low; Very Low} for the cost criteria (delivery and price) were converted to the following fuzzy numbers:{(0, 0, 3), (1, 3, 5), (3, 5, 7), (5, 7, 9), and (7, 10, 10)}, and the linguistic labels {Very Poor; Poor; Normal; Good; Very Good} for the benefit criteria (quality and service) were converted to the following fuzzy numbers: {(0, 0, 3), (1, 3, 5), (3, 5, 7), (5, 7, 9), and (7, 10, 10)}.