# Multicriteria Decision Making and Its Application in Geothermal Power Project
## 4 Case Study  
Geothermal energy has been exploited and used since the early 20 th century for the purpose of heating, drying agricultural products, relaxing, bathing, etc. Since then, research and development of technology to exploit energy sources has been carried out. Geothermal energy is growing rapidly in scale and efficiency. The building of geothermal power plants (due to their low cost and ecological cleanliness) has been quite popular in many countries, such as the US, China, France, New Zealand, Japan, Philippines, Canada, Australia, etc. If direct use is included, geothermal energy is being used in 70 countries around the world. Despite facing economic and technical challenges, geothermal energy scientists still forecast optimistically that geothermal exploitation will overcome the initial difficulties and will have an important place among the energy sources of the future. In Vietnam, according to a survey and evaluation of scientists, there are currently about 264 sources; hot springs are distributed relatively evenly across the country with an average temperature of 40-100 \({}^{\circ}\)C at a depth of 3 km. In addition, this energy source also has the advantage of being evenly distributed throughout the country, so it can be widely used in most localities, such as Phu Tho, Quang Binh, [PERSON], Quang Ngai, and Quang Tri [35]. In this research work, the author presents a fuzzy multicriteria decision-making approach to select an appropriate location for a geothermal power plant from five potential alternatives, Phu Tho (DMU1), Quang Binh (DMU2), [PERSON] (DMU3), Quang Ngai (DMU4), and Quang Tri (DMU5)). The three main criteria are physical suitable area, socioeconomic suitable area, and technical suitable area. A list of main criteria and sub-criteria is shown in Table 2; they are explained with proper consultation of the literature and expert opinions regarding how each criterion and sub-criterion was chosen according to its importance for determining a suitable geothermal power plant location. Although the AHP method is widely used, AHP often has limitations because of its incapability to combine the uncertainty and vagueness that always exists in establishing the mapping of perceptions, the decision maker's assessment, to exact numbers. To overcome these limitations, the author applied FAHP for determining the weight of criteria in the first stage of this study. A fuzzy comparison matrix based on experts' opinions and literature consultation for all criteria is shown in Table 3.  
In this work, the author utilized the triangular fuzzy number to convert the fuzzy numbers to real numbers (\(\alpha\) = 0.5 and \(\beta\) = 0.5). \(\alpha\) = 0.5 and \(\beta\) = 0.5 are chosen in this case to balance the change during the conversion between the fuzzy values and real values and to equally use both the geometrical value and summation of each assessment. \[\text{Q}_{0.5,0.5}(\overline{a_{PSA,TSA}})\ =\ [(0.5\ \times\ 3.5)+(1-0.5)\ \times\ 4.5]=4 \tag{22}\]  
\[\text{f}_{0.5}(\text{L}_{\text{PSA,TSA}})=(4-3)\ \times 0.5+3=3.5 \tag{23}\]  
\[\text{f}_{0.5}(\text{U}_{\text{PSA,TSA}})=5-(5-4)\ \times 0.5=4.5 \tag{24}\]  
\[\text{Q}_{0.5,0.5}(\overline{a_{TSA,PSA}})\ =\frac{1}{4} \tag{25}\]  
The real number priority when comparing the main criteria pairs is shown in Table 4. \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**No** & **Main Criteria** & **Sub-Criteria and Symbol** & **Literature Review** & **Experts** \\ \hline \multirow{4}{*}{1} & \multirow{4}{*}{Physical suitable area} & Slope (GPP01) & [PERSON] et al. [36] & X \\  & & Rivers (GPP02) & [PERSON] et al. [37] & X \\  & & Faults (GPP03) & [PERSON] et al. [38] & X \\  & & Population Centers (GPP04) & [PERSON] et al. [39] & X \\
2 & & area & Access Road (GPP05) & [PERSON] et al. [40] & X \\  & & Anomaly Zone (GPP06) & [PERSON] et al. [41] & X \\
3 & & Well Locations (GPP07) & [PERSON] et al. [42] & X \\  & & Hot Springs (GPP08) & [PERSON] et al. [43] & X \\ \hline \hline \end{tabular}
\end{table} 
Table 2: List of criteria.