## 3 Research Methodology  
### Analytic Hierarchy Process  
The AHP is a multicriteria decision-making method proposed by [PERSON] [47]. In the AHP, pairwise comparison is performed to generate criteria weights. Before calculating the weights, consistency index tests are conducted to determine the ranking of the criteria and select the optimal solution. In the AHP, a series of factors (criteria) that influence the target are analyzed, and pairwise comparison is performed between factors to determine the weight and decision-making priority of each problem. The results of the AHP can assist decision makers in selecting the optimal solution. The AHP can be used to process uncertain or subjective data to develop a hierarchical structure based on logical relationships. Such a structure enables decision makers to understand the relationships between each relevant factor, which allows for the analysis of additional criteria and the calculation of factor weights. The AHP is a multiple-attribute assessment method that can be used to divide complicated problems into attributes in a hierarchy. Accordingly, a hierarchical framework can be established on the basis of decision-making objectives, which can then be used to establish the hierarchical relationships between decision-making criteria. According to the number of factors in the hierarchy, each criterion can be further divided into subcriteria. The choicesfor assessment are presented at the bottom of the hierarchy. Pairwise comparison is conducted to determine the relative importance of two factors on the same layer (dimension) to a specific factor on a higher layer. The importance is rated on a scale of 1-9, and pairwise comparison matrices are developed. The eigenvectors of each comparison matrix are then obtained and multiplied with the importance rating of each factor to determine the factor weights, which are subsequently used to obtain the total score of each choice. In the AHP, interactions between factors on the same layer (dimension) are presented using arrows arranged in a circular form. The relationships between factor priorities must exhibit the properties of transitivity (i.e., if A is better than B and B is better than C, then A must dominate C) and strength (i.e., if A is two times better than B and B is three times better than C, then A must be six times better than C). However, given that complete transitivity between factors is rare, factors that exist intransitivity are acceptable if they pass the consistency ratio test. In the AHP, the relative importance of factors in each hierarchy is calculated to establish pairwise comparison matrices. The results of the pairwise comparison of the factors are assessed on a scale of 1-9. After assessment by experts and scholars, the comparison results for the importance of each factor are presented in the pairwise comparison matrix A, which is expressed as follows:  
\[\text{A}=\left[a_{ij}\right]= \begin{bmatrix}w_{1}/w_{1}&w_{1}/w_{2}&\cdots&w_{1 }/w_{j}&\cdots&w_{1}/w_{n}\\ w_{2}/w_{1}&w_{2}/w_{2}&\cdots&w_{2}/w_{j}&\cdots&w_{2}/w_{n}\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ w_{j}/w_{1}&w_{j}/w_{2}&\cdots&w_{j}/w_{j}&\cdots&w_{j}/w_{n}\\ \vdots&\vdots&\vdots&\vdots&\vdots&\vdots\\ w_{n}/w_{1}&w_{n}/w_{2}&\cdots&w_{n}/w_{j}&\cdots&w_{n}/w_{n}\\ \end{bmatrix}  \tag{1}\]  
where \(a_{ij}=w_{i}/w_{j}\), and \(w_{i}\) and \(w_{j}\) represent the weights of \(i\) factor and \(j\) factor, respectively. Given that \(a_{ij}=1/a_{ji}\), A is considered a positive reciprocal matrix. If all pairwise comparison values exhibit transitivity, then A is considered a consistent matrix. After establishing the pairwise comparison matrix, numerical analysis is conducted using eigenvalue solutions to obtain the eigenvector of this matrix. According to the theory of numerical analysis, if A is an \(n\times n\) consistent matrix, the relationship between the eigenvector (X) and eigenvalue (\(\lambda\)) of matrix A can be expressed as presented in Equation (2). Equation (3) is obtained through the transposition of Equation (2).