Step 1: According to the RE overseas investment project risk assessment indicator system, determine the mutual influence relationship between indicators and construct the ANP structure of RE overseas investment project risk assessment accordingly.

Based on relevant literature, this article divides the risk factors affecting China’s foreign investment in renewable energy into three aspects: political risk, economic risk, and project risk. According to the composition of risk factors, they are divided into 26 indicators in total. The indicator system can be seen in Appendix 1.

Step 2: Calculate the supermatrix and weighted supermatrix of the ANP structure. the judgment matrices of first-level indicators, second-level indicators and third-level indicators are constructed respectively, and the characteristic vectors of the second-level indicators $\left(w_{1k},w_{2k},\cdots ,w_{mk}\right)$ and the characteristic vectors of the third-level indicators are formed.

When the eigenvector of the secondary index u_ij passes the consistency test, it is expressed in matrix form to generate a local weight vector matrix W_ij. Under the influence of the first-level index u_i,m super matrices W, and W is not a normalized matrix. In the matrix, each element represents a matrix, and the column sum is I, as shown in formula (1). The supermatrix W column is normalized to obtain the weighted ultra-short matrix $\bar{W}={\left(W\right)}_{m\times m}$, where $\bar{W}={\alpha }_{ij}\times W_{ij}$, ${\alpha }_{ij}$ is the weighted factor.

$\bar{W}=\left[\begin{array}{cccc}{w}_{11}& w_{12}& \cdots & w_{1k}\\ w_{21}& w_{22}& \cdots & w_{2k}\\ ⋮& ⋮& \ddots & ⋮\\ w_{m1}& w_{m2}& \cdots & w_{mk}\end{array}\right]$ (1)

When the eigenvector of the third-level indicator passes the consistency test, a local weight vector, i.e., a matrix, is generated. K super matrices are formed under the influence of the second-level indicator, and the super matrix columns are normalized to obtain a reinforcement matrix, as shown in Formula (2).

$W=\left[\begin{array}{cccc}{w}_{111}& w_{112}& \cdots & w_{11n}\\ w_{211}& w_{212}& \cdots & w_{2k}\\ ⋮& ⋮& \ddots & ⋮\\ w_{m1}& w_{m2}& \cdots & w_{mk}\end{array}\right]$ (2)

Step 3: Calculate the limit permutation sorting vector of the third level indicator weighted supermatrix $\overline{w^{\prime }}$, as shown in formula (3), and stabilize the weighted supermatrix. When i tends to infinity and the limit convergence is unique, the limit matrix $W^{\infty }\text{'}$ of the indicators will be generated. The column vectors in the limit matrix $W^{\infty }\text{'}$ are the weights of each indicator.

$W^{\infty }\text{'}=\underset{j\to \infty }{\lim }\left(\frac{1}{k}\right)\underset{j=1}{\overset{k}{{\displaystyle \sum }}}{\bar{W}}_j$ (3)

The column vectors in the limit matrix $W^{\infty }$ are the weights of each second-level indicator.

$W^{\infty }=\underset{i\to \infty }{\lim }\left(\frac{1}{m}\right)\underset{i=1}{\overset{m}{{\displaystyle \sum }}}{\bar{W}}_i$ (4)

Step 4: Let the assessment set be $\left(l_1,l_2,\cdots ,l_v\right)$, The evaluator evaluates and scores each of the thrird-level indicators based on the assessment set. According to the assessment level of the third-level indicators, the assessment set of this paper $\left(l_1,l_2,\cdots ,l_5\right)=\left(\text{outstanding},\text{exerllent},\text{good},\text{common},\text{bad}\right)$.

Evaluation grades and standards of indicators can be seen in the appendix. Summarize third-level indicator assessment vector $\left(b_{ijh1},b_{ijh2},\cdots ,b_{ijhv}\right)$. $f_{ijhl}$, is the total number of times the third-level indicator $u_{ijh}$ is evaluated as level $l_v$, and $b_{ijhl}$ is the membership degree of the third-level indicator classified to the assessment level

$b_{ijhl}=\frac{f_{ijhl}}{{{\displaystyle \sum }}_{l=1}^v{f}_{ijhl}}$ (5)

The assessment matrix of the second-level indicators is constructed based on the assessment vector of the third-level indicators, as shown in formula 6.

$B_{ij}=\left[\begin{array}{c}{B}_{ij1}\\ B_{ij2}\\ ⋮\\ B_{ijh}\end{array}\right]=\left[\begin{array}{cccc}{b}_{ij11}& b_{ij12}& \cdots & b_{ij1v}\\ b_{ij21}& b_{ij22}& \cdots & b_{ij2v}\\ ⋮& ⋮& & ⋮\\ b_{ijk1}& b_{ijh2}& \cdots & b_{ijhv}\end{array}\right]$ (6)

The third-level indicator weights and the second-level indicator assessment matrix determined by the ANP method $B_{ij}$, Calculate the assessment vector $P_{ij}$ of the secondary index $u_{ij}$. Since the number of indicators is big, weighted average operator is used M in the fuzzy calculation, see formular (7). According to the membership principle of fuzzy mathematics, the maximum membership $b_{ijv}$ corresponding assessment level is the assessment result of the indicator.

$\begin{array}{c}{P}_{ij}=W_{ij}\otimes B_{ij}=\left(w_{ij1},w_{ij2},\cdots ,w_{ijh}\right)\otimes \left[\begin{array}{cccc}{b}_{ij11}& b_{ij12}& \cdots & b_{ij1v}\\ b_{ij21}& b_{ij22}& \cdots & b_{ij2v}\\ ⋮& ⋮& & ⋮\\ b_{ijh1}& b_{ijh2}& \cdots & b_{ijhv}\end{array}\right]\\ =\left(b_{ij1},b_{ij2},\cdots ,b_{ijv}\right)\end{array}$ (7)

Based on the assessment vector $P_{ij}$ of the secondary index, the assessment matrix Bi of the primary index is constructed, as shown in formula (8).

$B_i=\left[\begin{array}{c}{P}_{i1}\\ P_{i2}\\ ⋮\\ P_{ij}\end{array}\right]=\left[\begin{array}{cccc}{b}_{i11}& b_{i12}& \cdots & b_{i1v}\\ b_{i21}& b_{i22}& \cdots & b_{i2v}\\ ⋮& ⋮& & ⋮\\ b_{ij1}& b_{ij2}& \cdots & b_{ijv}\end{array}\right]$ (8)

The second-level indicator weights and the first-level indicator assessment matrix Bi can be determined according to the ANP method,

Calculate assessment vector $P_i$ see formula (9).

$P_i=W_i\otimes B_i=\left(w_{i1},w_{i2},\cdots ,w_{ij}\right)\otimes \left[\begin{array}{cccc}{b}_{i11}& b_{i12}& \cdots & b_{i1v}\\ b_{i21}& b_{i22}& \cdots & b_{i2v}\\ ⋮& ⋮& & ⋮\\ b_{ij1}& b_{ij2}& \cdots & b_{ijv}\end{array}\right]=\left(b_{i1},b_{i2},\cdots ,b_{iv}\right)$ (9)

Based on the assessment vector $P_i$ of the first-level indicators, the overall assessment matrix $B$ is constructed, as shown in formula (10).

$B=\left[\begin{array}{c}{P}_1\\ P_2\\ ⋮\\ P_i\end{array}\right]=\left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1v}\\ b_{21}& b_{22}& \cdots & b_{2v}\\ ⋮& ⋮& & ⋮\\ b_{i1}& b_{i2}& \cdots & b_{iv}\end{array}\right]$ (10)

According to the first-level indicator weights determined by the ANP method and the overall assessment matrix $B$, Overall assessment vector $P$ of REOIR is calculated, see formula (11). Here the assessment level lv corresponding to the maximum membership degree bv is the REOIR comprehensive score.

$P=W_i\otimes B_i=\left(w_1,w_2,\cdots ,w_i\right)\otimes \left[\begin{array}{cccc}{b}_{11}& b_{12}& \cdots & b_{1v}\\ b_{21}& b_{22}& \cdots & b_{2v}\\ ⋮& ⋮& & ⋮\\ b_{i1}& b_{i2}& \cdots & b_{iv}\end{array}\right]$ (11)

This paper uses the expert scoring method to determine the score of each indicator. The experts are composed of 1) invest managers of the National Development Bank, who are responsible for approving foreign investment loans. 2) Project manager and of Jinko Power. They have been directly involved in and followed up the project investment process, have the most comprehensive project knowledge, and are experts in the investment field. A total of 20 questionnaires were distributed, and 17 valid questionnaires were collected. Considering that the questionnaire survey method has a certain degree of subjectivity, this paper combines the practical data of the Global Corruption Index Report, CEIC’s economic databases, and the exchange rate, interest rate, and inflation index of the host country UAE in the past five years to test the objectivity of the questionnaire data.

According to the indicators system above-mentioned, combined with the relationship between each assessment index, this paper uses Excel software to calculate the weight of each level of indicators.

In the structural model of REOI assessment, experts in the industry are invited to judge and score in the order of criteria, sub-criteria, and indicators. In the software, the nine-point method is used to judge the relationship between two indicators, from 1 to 9, indicating that a certain indicator’s influence or relative importance on another indicator gradually increases. The score value of the judgment matrix is the average of the expert score value. The overseas investment risk level is used as the assessment criterion in the control layer. The judgment matrix is shown in the figure. The criteria weights are 0.433, 0.329 and 0.238, and the consistency test results are all passed. The sub-criteria weights under the A standard are 0.144 and 0.289, the sub-criteria weights under the B standard are 0.209, 0.085, and 0.034, and the weights under the C standard are 0.022, 0.062, 0.117, and 0.038, and the consistency test is passed. The weight results of each indicator are shown in Table 1 and Figure 1 .

To ensure that the assessment results can more effectively reflect the level of REOIR, experts and scholars in the industry are invited to evaluate and score the specific indicators (third-level indicators) of the investment risk of this project. Based on the three main risk sources, political risk, economic risk, and project risk, the evaluator ticks the corresponding level of the indicator in the assessment form according to the third-level indicator assessment level and standards. Each indicator can only correspond to one assessment level, and multiple selections or no selections are considered invalid. This assessment form was distributed via e-mail. A total of 7 assessment forms were distributed, 7 were collected within the specified time, and all were valid, with a successful rate of 100%. Among the experts and scholars participating in the assessment, 86% have the title of professor or professor-level senior engineer, and 70% are engaged in research in the field of smart grids. The corresponding number of times the third-level indicators were rated at each level was summarized and counted. The statistical results are shown in Table 2 .

According to Table 2 , the assessment results and grade times of each indicator are counted, and MATLAB software is used to perform a fuzzy linear transformation on the above data to form the assessment vector of each indicator, and the assessment matrix F_ij, of the indicator is constructed based on this. Here I = 1, 2, 3, 4; j = 1, 2, 3, 4, 5. Thus we can get the assessment matrix for Risks.