## 4 Case Study  
Located in the monsoon subtropical area with a long coastline, Vietnam has fundamental advantages for developing wind energy. When comparing the average wind speed in the East Sea of Vietnam and the surrounding sea areas, the result shows that wind in the East Sea of Vietnam is fairly strong and seasonally changes. A wind speed map of Vietnam is shown in Figure 4.  
For this research, the authors collected data from seven potential locations that are viable for wind power plants, as shown in Table 2.  
The AHP model with fuzzy logic is applied in the first stage of this work. A hierarchical structure to select the best location is built with four main criteria (including 12 sub-criteria). Completion of a questionnaire for analyzing the FAHP model is done by interviewing experts, and preferences from other research. The weight of each criteria is defined by the comparison matrix. The Hierarchical Structures for the FAHP approach are shown in Figure 5. \begin{table}
\begin{tabular}{c c c} \hline
**No** & **Locations** & **Symbol** \\ \hline
1 & [PERSON] & DMU1 \\
2 & [PERSON] & DMU2 \\
3 & [PERSON] & DMU3 \\
4 & [PERSON] & DMU4 \\
5 & [PERSON] & DMU5 \\
6 & [PERSON] & DMU6 \\
7 & [PERSON] & DMU7 \\ \hline \end{tabular}
\end{table} 
Table 2: Seven potential locations for building wind power plants in Vietnam. Figure 4: Wind speed map of Vietnam [40]. A fuzzy comparison matrix for GOAL from the FAHP model is shown in Table 3.  
The fuzzy numbers were converted to real numbers by using the TFN. During the defuzzification, the authors obtain the coefficients \(\alpha=0.5\) and \(\beta=0.5\) ([PERSON] and [PERSON]) [41]. In it, \(\alpha\) represents the uncertain environment conditions, and \(\beta\) represents the attitude of the evaluator is fair. \[ \begin{array}{c}\mathbb{g}_{0.5,0.5}(\overline{a_{EC,SC}})=[(0.5\times 2.5)+(1 -0.5)\times 3.5]=3\\ \mathbb{f}_{0.5}(\mathbb{L}_{EC,SC})=(3-2)\times 0.5+2=2.5\\ \mathbb{f}_{0.5}(\mathbb{U}_{EC,SC})=4-(4-3)\times 0.5=3.5\\ \mathbb{g}_{0.5,0.5}(\overline{a_{SC,EC}})=1/3\end{array} \]  
The remaining calculations for others criteria are similar to the above calculation. The real number priority when comparing the main criteria pairs are shown in Table 4.  
For calculating the maximum individual value as following:  
\[ \begin{array}{c}\text{OA1}=(1\times 3\times 4\times 3)^{1/4}=2.44\\ \text{OA2}=(1/3\times 1\times 2\times 5)^{1/4}=1.35\\ \text{OA3}=(1/4\times 1/2\times 1\text{ x }2)^{1/4}=0.71\\ \text{OA4}=(1/3\times 1/5\times 1/2\times 1)^{1/4}=0.43\end{array} \] \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Criteria** & **Economic (EC)** & **Environmental (SC)** & **Social (SO)** & **Technological (TE)** \\ \hline Economic (EC) & 1 & 3 & 4 & 3 \\ Environmental (SC) & \(1/3\) & 1 & 2 & 5 \\ Social (SO) & \(\frac{1}{4}\) & \(1/2\) & 1 & 2 \\ Technological (TE) & \(1/3\) & \(1/5\) & \(1/2\) & 1 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Real number priority. Figure 5: Hierarchical structures of the Fuzzy Analytic Hierarchy Process (FAHP) model. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Criteria** & **Economic (EC)** & **Environmental (SC)** & **Social (SO)** & **Technological (TE)** \\ \hline Economic (EC) & (1,1,1) & (2,3,4) & (3,4,5) & (2,3,4) \\ Environmental (SC) & (1/4,1/3,1/2) & (1,1,1) & (1,2,3) & (4,5,6) \\ Social (SO) & (1/5,1/4,1/3) & (1/3,1/2,1) & (1,1,1) & (1,2,3) \\ Technological (TE) & (1/4,1/3,1/2) & (1/6,1/5,1/4) & (1/3,1/2,1) & (1,1,1) \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Fuzzy comparison matrices for GOAL. \[\sum OA=\text{OA}1+\text{OA}2+\text{OA}3+\text{OA}4=4.9\]  
\[\omega_{1}=\frac{2.44}{4.93}=0.49\]  
\[\omega_{2}=\frac{1.35}{4.93}=0.27\]  
\[\omega_{3}=\frac{0.71}{4.93}=0.14\]  
\[\omega_{4}=\frac{0.43}{4.93}=0.09\]  
\[\left[ \begin{array}{rrrr}1&3&4&2\\ 1/3&1&2&5\\ 1/4&1/2&1&2\\ 1/3&1/5&1/2&1\end{array} \right]\times\left[ \begin{array}{rrrr}0.49\\ 0.27\\ 0.14\\ 0.09\end{array} \right]=\left[ \begin{array}{rrrr}2.04\\ 1.16\\ 0.58\\ 0.38\end{array} \right]\]  
\[\left[