## 2 Materials and Methods
### Research Framework
#### 2.3.2 Geospatial Analysis  
The second approach was the geospatial analysis to map RE resources available in the study areas. It assessed environmental, technical, technological, and socio-economic factors. The determinant factors were used to identify the exclusion criteria and constraints for geospatial analysis that affect suitable locations for installing RE technologies. The methodology was based on the concept of the previous research [111].  
Spatial Analysis  
The geospatial analysis involves several methods such as surface analysis, geometric operations, and distance operations. As shown in Table 2 below, the exclusion criteria and constraints were applied regarding environmental, technical, technological, and socio  
Figure 4: Research framework.  
economic aspects. The specific reclassification values and corresponding suitability ratings for each criterion are provided in Table S2.  
Spatial Decision Support  
The steps of the fuzzy AHP method are summarized as follows [130; 133; 134]:  
Step 1. Determine the goal, alternatives, and criteria.  
* Create a pairwise comparison matrix (PCM) using Equation (1), where \(n\) is the number of criteria, \(\mathrm{w}_{i}\) denotes the weight for the \(i\) criterion, and \(\mathrm{a}_{ij}\) is the ratio of the weight of \(i\) and \(j\) criteria. \[\mathrm{a}_{ij}=\frac{\mathrm{w}_{i}}{\mathrm{w}_{j}}\] (1) where \(i,j=1,2,\ldots,n\). \[\mathrm{A}=\mathrm{a}_{ij}\frac{1}{\mathrm{a}_{ij}^{T}}\left[\begin{array}{ cccc}1&\mathrm{a}_{12}&\cdots&\mathrm{a}_{1n}\\ \mathrm{a}_{21}&1&\cdots&\mathrm{a}_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ \mathrm{a}_{n1}&\mathrm{a}_{n2}&\cdots&1\end{array}\right]\] (2)
* Convert [PERSON]'s numerical scale into a triangular fuzzy number (TFN). The FAHP scale has three values, the lower limit (l), medium limit (m), and the upper limit (u). Table 3 shows the linguistic values and the TFNs.
* Calculate the geometric mean using Equation (3), where \(\mathrm{l}_{ij}\), \(\mathrm{m}_{j}\), \(\mathrm{u}_{ij}\) are geometric means in the TFN scale, and k is the number of decision-makers. The TFN matrix is consistent if the value of \(1\leq\mathrm{m}\leq\mathrm{u}\). \[\mathrm{l}_{ij}=\left(\prod_{k=1}^{K}\mathrm{l}_{ijk}\right)^{\frac{1}{k}},\] \[\mathrm{m}_{ij}=\left(\prod_{k=1}^{K}\mathrm{m}_{ijk}\right)^{\frac{1}{k}},\] (3) \[\mathrm{u}_{ij}=\left(\prod_{k=1}^{K}\mathrm{u}_{ijk}\right)^{\frac{1}{k}}\]
* When the AHP numerical scale has been converted to FAHP scale values, calculate the fuzzy synthesis value (\(\mathrm{S}_{i}\)) given by Equations (4)-(6): \[\sum_{i=j}^{m}\mathrm{M}_{gi}^{j}=\left(\sum_{i=j}^{m}\mathrm{l}_{i},\;\sum_{ i=1}^{n}\mathrm{m}_{i},\;\sum_{i=j}^{m}\mathrm{u}_{i}\right)\] (4) \[\frac{1}{\left(\sum_{i=j}^{m}\sum_{i=1}^{n}\mathrm{M}_{gi}^{j} \right)}=\frac{1}{\sum_{i=1}^{n}\mathrm{u}_{i}},\;\frac{1}{\sum_{i=1}^{n} \mathrm{m}_{i}},\;\frac{1}{\sum_{i=1}^{n}\mathrm{l}_{i}}\] (5) \[\mathrm{S}_{i}=\sum_{j=1}^{m}\mathrm{M}_{gi}^{j}*\frac{1}{\left(\sum_{i=j}^{m }\sum_{i=1}^{n}\mathrm{M}_{gi}^{j}\right)}\] (6)
* The last step is to calculate the crisp weights. It can be obtained through a defuzzification process as defined by: \[\mathrm{W}_{j}=\frac{1+\mathrm{m}+\mathrm{u}}{3}\] (7)
* Calculate the eigenvector, maximum eigenvalue, Consistency Index (CI), and the consistency ratio (CR) using Equations (8)-(10), where \(\mathrm{\lambda}_{\mathrm{max}}\) is the eigenvalue of paired comparison matrix, and RI is for random index (Table 4). \[\mathrm{\lambda}_{\mathrm{max}}=\frac{\sum\mathrm{Ratio}}{\mathrm{n}}\] (8) \[\mathrm{CI}=\frac{\mathrm{\lambda}_{\mathrm{max}}-\mathrm{n}}{ \mathrm{n}-1}\] (9)  
* Calculate the performance score (CP) of each alternative to the positive ideal solution (A\({}^{+}\)). \[\text{CP}_{\text{i}}=\frac{\text{d}_{\text{i}}^{-}}{\left(\text{d}_{\text{i}}^{ +}+\text{d}_{\text{i}}^{-}\right)}\] (17)
* Rank the alternatives according to the performance score, where the shortest distance is the positive ideal solution, and the farthest distance is the negative ideal solution.