## 3 Study Methods and Evaluation Process
### Determination of Index Weight
#### 3.2.1 Rough Set Theory  
Rough set (\(R\)s) theory is a theoretical method proposed by [PERSON] et al. (2015) to study the expression, learning and generalization of incomplete and uncertain knowledge and data. It can mine potential and useful knowledge from a large amount of data and reduce the unnecessary workload of calculation and classification caused by redundant knowledge. In Rs theory, membership is no longer an initial concept but an objectively \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \multirow{2}{*}{**Criterion Layer \(B_{i}\)**} & \multirow{2}{*}{**Index Layer \(C_{i}\)**} & \multicolumn{4}{c}{**Underground Space Development Geological Suitability Grade**} \\  & & **I** & **II** & **III** & **IV** & **V** \\  & & \(\geq\)**90** & **90 \(\times\)\(x\)\(\geq\) 80** & **80 \(\times\)\(x\)\(\geq\) 70** & **70 \(\times\)\(x\)\(\geq\) 60** & **\textless60** \\ \hline \multirow{4}{*}{Geotechnical characteristics \(B_{1}\)} & Compression coefficient of soil mass/MPa\({}^{-1}\) C & \textless{}0.1 & 0.1–0.3 & 0.3–0.5 & 0.5–0.7 & \textless{}0.7 \\  & Rock/soil bearing capacity/MPa C & \(\geq\)0.4 & 0.3–0.4 & 0.2–0.3 & 0.1–0.2 & \textless{}0.1 \\  & Soil uniform C\({}_{3}\) & Uniform & More uniform & Less uniform & Nonuniform & - \\ \hline \multirow{4}{*}{**Target layer \(D\)**} & \multirow{4}{*}{Geomorphology \(B_{2}\)} & \multirow{4}{*}{Landform unit C\({}_{4}\)} & \multirow{4}{*}{Hill} & \begin{tabular}{c} Erosion and accumulation of \\ low ridge \\ \end{tabular} & \begin{tabular}{c} Alluvial \\ plain \\ 20–30 \\ \end{tabular} & \begin{tabular}{c} Al alluvial \\ lasttime \\ plain \\ 30–50 \\ \end{tabular} & \begin{tabular}{c} Lactustrine \\ plain \\ 250 \\ \end{tabular} \\ \cline{1-1}  & & Topographic slope/\% C\({}_{5}\) & \textless{}10 & 100–20 & 800–500 & 500–200 & \textless{}200 \\ \cline{1-1}  & & Fault/m C\({}_{6}\) & \(\geq\)1000 & 1000–800 & 800–500 & 500–200 & \textless{}200 \\ \cline{1-1}  & Seismic basic intensity C\({}_{7}\) & \(\leq\)VI & VII & VIII & IX & \textgreater{}X \\ \hline \multirow{4}{*}{Hydroogeology \(B_{4}\)} & The depth of & & & & & \\ \cline{1-1}  & confined water & \(\geq\)18 & 16\(\sim\)18 & 14–16 & 10–14 & \textless{}10 \\ \cline{1-1}  & \begin{tabular}{c} Proof/m C\({}_{8}\) \\ water inflow of \\ single well-t\({}^{-1}\) C\({}_{9}\) \\ Groundwater \\ corrosion C\({}_{10}\) \\ \end{tabular} & \begin{tabular}{c} 100–400 \\ \end{tabular} & \begin{tabular}{c} 400–700 \\ \end{tabular} & \begin{tabular}{c} 700–1000 \\ \end{tabular} & \
\begin{tabular}{c} \(\geq\)1000 \\ \end{tabular} \\ \cline{1-1}  & & & & & & \\ \hline \multirow{4}{*}{Adverse geological phenomenon \(B_{5}\)} &
\begin{tabular}{c} Karst ground \\ collapse C\({}_{11}\) \\ Soft soil \\ settlement C\({}_{12}\) \\ \end{tabular} & No & Weak & Medium & - & Strong \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Index selection and quantification classification. \begin{table}
\begin{tabular}{c c} \hline \hline \multicolumn{1}{c}{**Rank**} & \multicolumn{2}{c}{**Membership**} \\ \hline I & & (0.75, 0.25, 0, 0, 0) \\ II & & (0.15, 0.7, 0.15, 0, 0) \\ III & & (0.15, 0.7, 0.15, 0) \\ IV & & (0, 0.15, 0.7, 0.15) \\ V & & (0, 0, 0.15, 0.7, 0.15) \\ V & & (0, 0, 0, 0.25, 0.75) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Membership degree of qualitative indicators. calculated one, which is only related to known knowledge, thus avoiding the influence of subjective factors [26; 27; 28]. In rough set theory, an information table is a basic tool to express and process knowledge [29]. The basic component of the information table knowledge expression system is the collection of research objects. The knowledge about these objects is described by specifying the attributes (characteristics) of objects and their attribute values. Generally, an information table knowledge expression system S can be expressed as:  
\[S=<U,R,V,f> \tag{1}\]  
where \(U\) is the set of objects, also known as the domain, \(R=C\cup D,\ C\cap D=\Phi,C\) is the set of conditional attributes and \(D\) is the set of decision attributes.