# Suitability Evaluation of Urban Underground Space Development: A Case Study of Qingdao City
## 3 Research Method
### Weight Assignment of Evaluation Indicators
Considering the characteristics of the variable weight status function and its derivative discussed in the preceding section and integrating the features of urban underground space development in Qingdao City and the developed underground spaces in the main urban area, we determine \(d=0.4\), \(e=0.5\), and \(f=0.7\). The resulting function is as follows:  
\[Y(X)= \begin{cases}0.25\ln\frac{0.25}{x_{i}}+0.75,&x_{i}e(0,0.25)\\ 0.9-x_{i},&x_{i}e(0.25,0.5)\\ 25{x_{i}}^{2}-3x_{i}+1.3,&x_{i}e(0.5,0.75)\\ 0.4,&x_{i}e(0.75,1)\end{cases}  \tag{3}\]  
Utilizing the variable weight theory along with \(W^{0}\) and \(Y(X)\), we derive the variable weightings for each evaluation indicator within the fundamental evaluation units. Given the considerable computational complexity involving matrix operations, this necessitates the use of MATLAB R2023b programming to facilitate implementation. The output results are presented in Table 3 below. The indicator weights obtained using both the variable-weight hierarchical analysis method and the traditional hierarchical analysis method are summarized, and preliminary evaluation scores are calculated. Figures 6 and 7 depict scatter plots showing the evaluation scores for shallow underground spaces in the research area, generated using the multi-objective linear weighting method. The horizontal axis indicates the magnitude of the evaluation scores, while the vertical axis represents the frequency of occurrence for each score. Table 4 provides a comparative overview of the weighting results derived from the two variable-weight hierarchical analysis methods and the traditional method. Figure 5: Local state variable weight function. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Evaluation Unit** & **1** & **2** & **3** & **12,949** & **12,950** & **12,951** \\ \hline Population density & 0.029 & 0.018 & 0.041 & 0.027 & 0.029 & 0.028 \\ Transportation accessibility & 0.116 & 0.064 & 0.164 & 0.096 & 1.000 & 0.090 \\ Commercial land price & 0.038 & 0.032 & 0.047 & 0.084 & 0.057 & 0.045 \\ Elevation & 0.020 & 0.019 & 0.016 & 0.016 & 0.017 & 0.016 \\ Slope & 0.004 & 0.004 & 0.003 & 0.003 & 0.003 & 0.003 \\ Topographic features & 0.030 & 0.029 & 0.028 & 0.025 & 0.030 & 0.027 \\ Hydrophilicity & 0.027 & 0.026 & 0.022 & 0.023 & 0.024 & 0.021 \\ Surface water system & 0.055 & 0.052 & 0.044 & 0.045 & 0.047 & 0.074 \\ Existing buildings & 0.132 & 0.127 & 0.107 & 0.109 & 0.130 & 0.117 \\ Soft soil layer thickness & 0.274 & 0.263 & 0.221 & 0.258 & 0.236 & 0.213 \\ Rock and soil type & 0.137 & 0.131 & 0.110 & 0.113 & 0.118 & 0.106 \\ Active fracture & 0.070 & 0.117 & 0.099 & 0.101 & 0.105 & 0.167 \\ Disasters such as landslides and collapses & 0.070 & 0.117 & 0.099 & 0.101 & 0.105 & 0.095 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Weighting results of the Analytic Hierarchy Process with variable weights for evaluation units. Figure 6: Comparison of weighting methods for shallow underground spaces: (**a**) score of Analytic Hierarchy Process; (**b**) score of Variable-Weight Analytic Hierarchy Process. Figure 7: Comparison of weighting methods for medium and deep underground spaces: (**a**) score of Analytic Hierarchy Process; (**b**) score of Variable-Weight Analytic Hierarchy Process. From the graph, it can be observed that the comprehensive scores of shallow underground spaces obtained using the hierarchical analysis method mainly range from 0.6 to 0.95, with the overall center of gravity leaning towards the high-score region. The majority of the area falls within the high-score range, indicating a relatively concentrated distribution of evaluation results. In contrast, the distribution of comprehensive scores for shallow underground spaces obtained using the variable-weight hierarchical analysis method ranges from 0.5 to 0.9. According to the data in Table 3, it can be noted that the standard deviation is slightly higher compared to the former method.