## 2 Research Objective and Methodology
### Analytic Hierarchy Process Method  
Weight determination is one of the most critical components for evaluating RCI development level. AHP is a common decision-making method with multiple criteria. It was developed by [PERSON] in the 1970s to assist in solving complex decision problems by capturing both subjective and objective evaluation measures [34]. The fundamental approach of AHP is based on defining the big problem as a hierarchical structure, with the small problems being located in the lower levels. Thus, the solutions to the small problems are aggregated to form a solution for the big problem [35]. The steps are as follows [36]:  
(1) Construction of a hierarchy-type structure: Divide the evaluation object into a target layer (A), a dimension layer (A_i_), and an index layer (A_ij_). (2) Pairwise comparison: AHP uses a pair-wise comparison of the criteria importance with respect to the goal. In this paper, using the importance scale suggested by [PERSON] was employed to make a comparison about the importance of the different dimensions and indicators [34], as shown in Table 1. Through analysis of questionnaire results combined with the experts' evaluation of this field, a judgment matrix was built. The size of the comparison matrix (A) is n \(\times\) n, where n is the number of criteria relative to a specific criterion. \[\mathrm{A}=\left[ \begin{array}{cccc}a_{11}&a_{12}&\cdots&a_{1n}\\ a_{21}&a_{22}&\cdots&a_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a_{n1}&a_{n2}&\cdots&a_{nn}\end{array} \right] \tag{1}\]  
The pairwise comparison matrix is indicated as \(\mathrm{A}=\left(a_{ij}\right)_{n\times n}(i,j=1,2,\cdots n)\), and satisfies:\[a_{ij}=\left\{ \begin{array}{ll}1/a_{ji}&i\
eq j\\ 1&i=j\end{array} \right. \tag{2}\]  
where \(a_{ij}\) represents the relative importance of \(a_{i}\) over \(a_{j}\). (3) Consistency assurance: Saaty defined a consistency index (CI), which is computed for each matrix size from relevant values [34]. The consistency ratio (CR) is defined as the ratio between the CI of a given matrix and the CI of a same-size reference matrix containing random values. To check for consistency, A\({}^{\prime}\) matrix is calculated where A\({}^{\prime}\) is the normalized matrix of A:  
\[\text{A}^{\prime}=\left[ \begin{array}{cccc}a^{\prime}_{11}&a^{\prime}_{12} &\cdots&a^{\prime}_{1n}\\ a^{\prime}_{21}&a^{\prime}_{22}&\cdots&a^{\prime}_{2n}\\ \vdots&\vdots&\ddots&\vdots\\ a^{\prime}_{n1}&a^{\prime}_{n2}&\cdots&a^{\prime}_{mn}\end{array} \right] \tag{3}\]  
where \(a^{\prime}_{ij}=\frac{a_{ij}}{\sum_{i=1}^{n}a_{ij}},i,j=1,\,2,\,3,\ldots,\,n\). Then, the Eigen value and Eigen vect or were computed by Equations (4) and (5). \[\text{W}=\left[ \begin{array}{c}W_{1}\\ W_{2}\\ \vdots\\ W_{n}\end{array} \right],\text{and }W_{i}=\frac{\sum_{i=1}^{n}a^{\prime}_{ij}}{n}\text{ and }W^{\prime}=AW=\left[ \begin{array}{c}W^{\prime}_{1}\\ W^{\prime}_{2}\\ \vdots\\ W^{\prime}_{n}\end{array} \right] \tag{4}\]  
\[\lambda_{max}=\frac{1}{n}\bigg{(}\frac{W^{\prime}_{1}}{W_{1}}+\frac{W^{ \prime}_{2}}{W_{2}}+\ldots+\frac{W^{\prime}_{n}}{W_{n}}\bigg{)} \tag{5}\]  
where \(W\) is the Eigen vector, \(W_{i}\) is Eigen value of the given matrix and \(\lambda_{max}\) is the largest Eigenvalue value of the pair-wise comparison matrix. According to [PERSON], it is safe to assume that the largest Eigenvalue is greater than or equal to \(n\) (\(\lambda_{max}\ \geq n\)). The closer \(\ \lambda_{max}\) is to \(n\), the more consistent A is. The consistency ratio (CR) is calculated by AHP as:  
\[\text{Consistency index (CI)}=\frac{\lambda_{max}-n}{n-1} \tag{6}\]  
\[\text{Consistency ratio (CR)}=\frac{\text{CI}}{\text{Random index (RI)}} \tag{7}\]  
where RI is the random consistency index related to the dimension of matrix listed in Table 2.