## 3 Research Process and Methods
### Constructing the AHP Judgment Matrix
In addition, a scale from 1 to 9 is included in the criterion to quantify the difference in importance between the two. The scale values follow the principle of symmetry: when the elements are of equal importance, they are assigned a value of 1, and when there is a significant difference in importance, they are assigned a value of 9 [63]. The specific scaling criteria are detailed in Table 5.  
The maximum feature root \(\uplambda\)max is calculated using the eigenvector method, the eigenvector W is normalized, and the reasonableness of the judgment logic is verified according to the consistency ratio CR value. The judgment matrix passes the consistency test when the CR < 0.1, and, if it does not meet the requirements, the consistency test needs to be performed again [64]. The calculation process is shown in Equations (1)-(3), where n is the order of the matrix, \(\mathrm{a_{\bar{ij}}}\) is the element of the jth row and jth column, and \(\mathrm{w_{i}}\) is the corresponding eigenvector element. calculated using this formula. The \(\uplambda\)max is the basis for the subsequent consistency test. Through the matrix eigenvalue decomposition and consistency verification mechanism, this method effectively reduces the influence of subjective judgment bias on weight allocation and provides a quantitative basis for prioritization decisions in interface design elements. \[\uplambda_{\mathrm{max}}=\frac{1}{\mathrm{n_{i}}}\sum_{i=1}^{n}\left(\frac{ \mathrm{a_{\bar{ij}}}}{\mathrm{w_{i}}}\right) \tag{1}\]  
\[CI=\frac{\uplambda_{\mathrm{max}}-n}{n-1} \tag{2}\]  
\[CR=\frac{CI}{RI} \tag{3}\]  
The research team strictly followed the AHP method, and the expert group carried out systematic pairwise comparison of the evaluation elements of the criterion layer to construct a judgment matrix with hierarchical characteristics. After the eigenvector normalization \begin{table}
\begin{tabular}{c c c} \hline \hline
**Judgment Scale** & **Definition** & **Explain** \\ \hline
1 & Equally important & Both factors are equally important \\
3 & Slightly important & One factor is slightly more important than another \\
5 & Significantly important & One factor is significantly more important \\
7 & Especially important & One factor is more important than another factor \\
9 & Extremely important & One factor is extremely important compared to \\  & & another factor \\
2, 4, 6, 8 & Median & Used as compromise values in situations between \\  & & the above judgment scales \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Scaled rating table. and weight calculation, the matrix formed the priority ranking of each indicator in the criterion layer. The results are shown in Table 6.  
According to the indicators in the table, the eigenvalue \(\lambda\)max is calculated as:  
\[\lambda\text{max}=(3.2402+3.2491+3.2483)/3=3.0385 \tag{4}\]  
According to the above steps, the consistency index CI is calculated:  
\[\text{CI}=(3.0385-3)/(3-1)=0.01925 \tag{5}\]  
According to Table 7, when the matrix order \(n=3\),  
\[\text{CR}=\text{CI}/\text{RI}=0.01925/0.58=0.0332<0.1 \tag{6}\]  
The stochastic consistency ratio CR calculated using this method is 0.0332, which is less than 0.10 and meets the consistency requirements, indicating that the program is effective [65]. On this basis, the comparison matrix is constructed and the secondary weight values of all sub-criteria-level indicators under the three criteria are calculated separately. The relevant judgment matrices and weight values are shown in Tables 8-10. The CR value of the three judgment matrices is less than 0.10, which meets the consistency test and reflects real expert opinion. \begin{table}
\begin{tabular}{c c c c c} \hline
**Index** & **B\({}_{1}\)** & **B\({}_{2}\)** & **B\({}_{3}\)** & **Single Layer Weight** \\ \hline \(\mathbf{B_{1}}\) & 1 & 3 & 5 & 0.6370 \\ \(\mathbf{B_{2}}\) & 1/3 & 1 & 3 & 0.2583 \\ \(\mathbf{B_{3}}\) & 1/5 & 1/3 & 1 & 0.1047 \\ \hline \end{tabular}
\end{table} 
Table 6: Weight of the quasi-layer.