## 4 Research Methodology
### Phase II Determination of the Weights of Criteria Based on DEMATEL Method  
The importance of the criteria on GPP technology selection is different, so the DEMATEL method is used to decide the weight of criteria in this phase. The direct and indirect causal relations among criteria are considered in the DEMATEL method, and the subjective judgment of DMs is also considered. The steps of determining the weights based on the DEMATEL method are shown as follows [28]:  
Step 1. Determine the influence factors in the system  
The influence factors of GPP technology selection system are determined based on expert opinions and literature reviews, which is called the criteria, as shown in Table 1.  
Step 2. Construct the direct-relation matrix among the criteria  
The direct-relation matrix \(X=\left(x_{pq}\right)_{n\times n}\) is constructed in stages, where \(x_{pq}\) is used to represent the degree of direct influence of \(p\)th criterion on \(q\)th criterion which is evaluated by the experts, and \(n\) is the number of criteria.  
Step 3. Normalize the direct-relation matrix  
The direct-relation matrix \(X=\left(x_{pq}\right)_{n\times n}\) is normalized into \(Y=\left(y_{pq}\right)_{n\times n}\). A normalization factor [29]\(s\) is applied in the normalized calculation, and the normalized direct-relation matrix \(Y\) is calculated by using Equations (1) and (2).  
\[Y=s\cdot X \tag{15}\]  
\[s=\text{Min}\Bigg{(}\frac{1}{\text{Max}_{1\leq p\leq n}\left(\sum_{q=1}^{n}x _{pq}\right)},\frac{1}{\text{Max}_{1\leq p\leq n}\left(\sum_{q=1}^{n}x_{pq} \right)}\Bigg{)} \tag{16}\]  
Step 4. Calculate the comprehensive-relation matrix.  
The comprehensive-relation matrix \(T\) is obtained by using Equation (3).  
\[T=\sum_{\lambda=1}^{\infty}Y^{\lambda}=Y(I-Y)^{-1} \tag{17}\]  
where \(T=\left(t_{pq}\right)_{n\times n}\), \(p,q=1,2,\cdot\cdot\cdot n\), and \(t_{pq}\) is used to represent the degree of total influence of \(p\)th criterion on \(q\)th criterion. \(I\) represents for the identity matrix.  
Step 5. Determine the influence relation among criteria  
The influence degree and influenced degree of the criteria is determined after obtaining the comprehensive-relation matrix \(T\). The sum of the row and column values of matrix \(T\) can be obtained by the Equations (4) and (5). The sum of row values of \(T\), denoted by \(D\), which represents the overall influence of a given criterion on other criteria. The sum of column values of \(T\), denoted by \(R\), which implies the overall influence of other criteria on a given criterion.  
\[D=\left(d_{p}\right)_{n\times 1}=\sum_{q=1}^{n}t_{pq} \tag{18}\]  
\[R=\left(r_{q}\right)_{1\times n}=\sum_{p=1}^{n}t_{pq} \tag{19}\]  
The causal diagram is obtained based on the \(D+R\) and \(D-R\) values. The \(D+R\) value indicates the importance of indicator in the SMPV plan selection system, the greater the \(D+R\) value, the more important the corresponding indicator is. On the other hand, the \(D-R\) value indicates the influence between a certain indicator and the other indicators, which can be separated into cause and effect groups. The indicator, which has positive values of \(D-R\), belongs to the cause group, and dispatches effects to the other indicators. Otherwise, the indicator, which has negative values of \(D-R\), belongs to the effect group, and receives effects to the other indicators.  
Step 6. Determine the weight of criteria  
The criteria are represented by \(j\), and satisfying \(j=1,\cdots p,\cdots q,\cdots n\), then the weights of criteria are determined based on the following Equations (6) and (7) [30].  
\[w_{j}^{\prime}=\left[\left(d_{j}+r_{j}\right)^{2}+\left(d_{j}-r_{j}\right)^{ 2}\right]^{1/2} \tag{20}\]  
\[w_{j}=\frac{w_{j}^{\prime}}{\sum_{j=1}^{n}w_{j}^{\prime}} \tag{21}\]  
where \(w_{j}^{\prime}\) denotes the relative importance of the indicators, and \(w_{j}\) denotes the weights of the indicators in SMPV technology selection.