## 2 Methodology
### Experimental Procedure
#### 2.3.2 Identification of Key Requirements  
In this study, AHP was applied to calculate the weights of various user needs for a product. Initially, the influencing factors at the decision-making level were analyzed, and a hierarchical model was constructed, progressing from the goal layer to the solution layer, as illustrated in Figure 4. A panel of experts was invited to evaluate each level of user need through pairwise comparisons using a scale of 1-9. The mean scores were calculated to derive judgment matrices. Based on these matrices, the geometric mean algorithm was used to calculate the weights of user needs. Consistency checks were conducted to ensure the rationality of the judgment matrix. Based on these weights, the key user needs with the highest rankings were identified, forming the basis for determining product design elements and guiding subsequent solution designs. The detailed calculation procedure is outlined in Equations (3)-(8):  
Step 1. Obtain the product of hierarchical needs \(M_{i}\):  
\[M_{i}=\prod_{j=1}^{m}b_{ij}=(i=1,2,\ldots,m;\ j=1,2,\ldots,n) \tag{3}\]  
Figure 4: AHP hierarchical model. where \(b\) represents the user requirement comparison matrix constructed in this study. The value in the \(i\) row and \(j\) column of the matrix is denoted as \(b_{ij}\), representing the relative importance of requirement \(i\) compared with requirement \(j\). The total number of requirement indicators is denoted as \(m\), and \(M_{i}\) represents the relative product value of indicator \(i\) with respect to all others, serving as the basis for weight calculation. In this study, the values of \(b_{ij}\) were derived from expert pairwise comparisons of demand topics extracted using the BTM model. Step 2. Obtain the geometric mean of the product of hierarchical needs \(a_{i}\):  
\[a_{i}=\sqrt[n]{M_{i}}(i=1,2,\ldots,m;\ j=1,2,\ldots,n) \tag{4}\]  
where \(a_{i}\) represents the overall priority of each user requirement topic aggregated from all expert judgments. Step 3. Obtain the relative weight, \(W_{i}\):  
\[W_{i}=\frac{a_{i}}{\sum_{i=1}^{m}\ a_{i}} \tag{5}\]  
where \(W_{i}\) denotes the relative weight of the \(i\) user requirement calculated using the geometric mean method. This weight reflects the importance of the requirement within the overall evaluation system. Step 4. In this study, experts constructed a pairwise comparison matrix based on multiple user comment topics extracted using the BTM model. To evaluate the consistency of this judgment matrix, it is necessary to calculate its maximum eigenvalue, \(\lambda_{\max}\). In AHP, if judgment matrix \(B\) and its corresponding weight vector \(W\) satisfy the relationship \(B\cdot W=\lambda_{\max}\cdot W\), then the ratio \(\frac{BW_{i}}{W_{i}}\) for each element should approximate \(\lambda_{\max}\). Accordingly, matrix \(B\) is first multiplied by weight vector \(W\) to obtain a new vector \(BW\). Each element of this vector is then divided by the corresponding component of \(W\), and the average of these ratios is calculated to estimate \(\lambda_{\max}\). This process is expressed as follows:  
\[\lambda_{\max}=\frac{1}{n}\sum_{i=1}^{n}\frac{BW_{i}}{W_{i}} \tag{6}\]  
where \(BW_{i}\) represents the \(i\) component of the product of judgment matrix \(B\) and weight vector \(W\), and \(n\) denotes the order of the judgment matrix, which corresponds to the number of user need topics evaluated for importance in this study. Step 5. A consistency check was conducted to validate the judgment matrix by calculating the consistency index (\(CI\)) and the consistency ratio (\(CR\)). \[CI=\frac{\lambda_{\max}-n}{n-1} \tag{7}\]  
\[CR=\frac{CI}{RI} \tag{8}\]  
where \(n\) denotes the order of the judgment matrix, \(RI\) denotes the random consistency index, and \(CR\) denotes the consistency ratio. When \(CR\leq 0.1\), the consistency check passes. At this point, expert judgments are considered valid, providing a reliable basis for the subsequent design process.