## 2 Data and Methods
### Methods
#### 2.2.1 Data Processing and Weight Decision  
The original data were first constructed into matrix \(A=\left[a_{ij}\right](i=1,2,3,4,j=1,2,\cdots,25)\). Then, we standardized it to matrix \(B=\left[b_{ij}\right](i=1,2,3,4,j=1,2,\cdots,25)\), which was used in the subsequent analysis.  
Different indicators play different roles in the total performance. The weights are determined by experts in the field. They were selected from Hubei Provincial Archives, Wuhan University Archives, School of Information Management at Wuhan University, National Archives Administration of China, School of Humanities at Nanchang University, and School of Information Resources Management in Renmin University of China. The results were obtained by Delphi analysis. The weight of the primary index was directly determined by the experts, while those of particular indicators were determined by AHP [22; 23]. AHP is a  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Primary Index** & **Indicators** & **Abbreviation** & **Weight (\%)** \\ \hline \multirow{6}{*}{Collection (25\%)} & Files & FIL & 5.13 \\  & Data & DAT & 2.56 \\  & Photos & PHO & 3.85 \\  & Audio tapes, video tapes, and film files & AVF & 3.85 \\  & Electronic archives & ELE & 5.13 \\  & Digital copy of library archives & DIG & 4.49 \\ \hline \multirow{6}{*}{Opening and utilization of archives (offline) (25\%)} & Open archives & OPE & 1.67 \\  & Reception file users & RFU & 3.33 \\  & Number of archives provided & NAP & 3.33 \\  & Reception users of government public & RUG & 2.67 \\  & information/current documents & & \\  & Number of government public & & \\  & information/current documents & NGP & 2.67 \\  & provided & & 1.00 \\  & Reception data user & RDU & 1.00 \\  & Quantity of data used & QDU & 1.00 \\  & Number of public access places for & PAG & 1.33 \\  & government information in archives & & 1.33 \\  & Number of patriotism education base in & PEB & 2.00 \\  & archives & AEH & 2.00 \\  & Number of archival exhibitions held & AEH & 2.00 \\  & Reception of exhibition & REE & 2.00 \\  & Publicly published materials & PPM & 2.00 \\ \hline \multirow{2}{*}{Floor space of archives (10\%)} & Total & TOT & 2.80 \\  & Storage Room & STR & 3.20 \\ \multirow{2}{*}{Digital archives certified by the competent archives department at or above the provincial level (15\%)} & Digital archives certified by the competent archives department at or above the provincial level & DAC & 15.00 \\ \hline \hline \end{tabular}
\end{table}
Table 1: _Cont._widely used multi-attribute decision-making method [24; 25; 26; 27; 28] that contains a judgment matrix \(W=\left[w_{ij}\right]\)\((i,j=1,2,\cdots,25)\), where \(w_{ij}\) describes the importance of the \(i\)th indicator compared with the \(j\)th indicator. Theoretically, the matrix can be derived from a certain weight vector and satisfies \(w_{ij}=w_{ik}\times w_{kj}\). However, the matrix determined by experts is often not completely self-consistent. Hence, we can get a none-zero value \(CI\) (consistency index), which can be expressed as follows:  
\[CI=\frac{\lambda_{max}-n}{n-1}, \tag{1}\]  
where \(\lambda_{max}\) and \(n=25\) are the highest eigenvalue and dimension of the matrix \(W\), respectively. We can claim that the consistency is acceptable if \(CI/RI<0.1\), where \(RI\) is a given index related to \(n\) and can be obtained by the random simulation of Saaty pair-wise comparison matrices [29]. The obtained weights are shown in Table 1.