## 3 Results
### Information Fusion of Micro Pore Parameters
\]  
According to differences between the GRG values of each index, a nine-level scaling method was established (Table 4), and a judgement matrix A was established based on Table 4. The judgement matrix A is presented in Table 5.  
Based on Equation (7), the eigenvector \(W\) is calculated as follows:  
\[ \begin{split} W_{PP}&=0.1139,W_{APD}=0.1187,W_{ASS} =0.0326,\\ W_{PSC}&=0.0724,W_{THC}~{}=0.3555,W_{Porosity}=0.1139,W_{ NWA}=0.1930\end{split} \]  
Table 4 is checked for consistency according to Equation (8), \(\lambda_{\text{max}}\) = 7.2499 CR = 0.0306 < 0.1. By comparing the eigenvector coefficient of each index, the indexes difference is as follows:  
\[W_{THC}~{}>~{}W_{NWA}>W_{APD}>W_{Porosity}=W_{PP}>W_{PSC}~{}>W_{ASS}\]  
The sandstone water-bearing capacity index calculation model was established in line with each index's eigenvector, and the equation is as follows:  
\[L=0.1139*app+0.1187*a_{APD}+0.0326a_{ASS}+0.0724*a_{PSC}~{}+0.3555*a_{THC}~{}+0. 1139*a_{Porosity}+0.193*a_{NWA} \tag{9}\]  
_L- The Sandstone water bearing capacity index_  
Equation (9) is the evaluation model of the water-bearing capacity of sandstone. The water-bearing capacity of three sandstone types in the study area was calculated and evaluated using this expression (Table 6). According to Table 6, the average water-bearing capacity index of sandstone in the Luo'he, Zhi'luo and Yan'an formations is 0.917, 0.423 and 0.076, respectively. The comparison index revealed that the water-bearing capacity of sandstone in the Luo'he and Zhi'luo formations was higher than that in the Yan'an formation. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Scale** & **Meaning** & **Expression of the GRG** \\ \hline
1 & The two factors have the same importance & 0 \textless{} G(n,i)-G(n,j) \textless{} 0.01 \\
2 & One factor was slightly important than the & 0.01 \textless{} G(n,i)-G(n,j) \textless{} 0.3 \\
3 & One factor is important to other factors & 0.03 \textless{} G(n,i)-G(n,j) \textless{} 0.06 \\
4 & One factor is more important than other & 0.06 \textless{} G(n,i)-G(n,j) \textless{} 0.09 \\
5 & One factor is much more important than & \\  & the other factors & G(n,i)-G(n,j) \textgreater{} 0.09 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Five-level scale method improved using the GRG. \begin{table}
\begin{tabular}{c c c c c c c c c} \hline \hline  & **PP** & **APD** & **ASS** & **PSC** & **THC** & **Porosity** & **NWA** & **Wi** \\ \hline PP & 0 & \(-0.009\) & 0.075 & 0.012 & \(-0.066\) & 0.000 & \(-0.024\) & 0.1139 \\ APD & 0.009 & 0 & 0.084 & 0.022 & \(-0.057\) & 0.010 & \(-0.015\) & 0.1187 \\ ASS & \(-0.075\) & \(-0.084\) & 0 & \(-0.063\) & \(-0.141\) & \(-0.075\) & \(-0.099\) & 0.0326 \\ PSC & \(-0.012\) & \(-0.022\) & 0.063 & 0 & \(-0.078\) & \(-0.012\) & \(-0.037\) & 0.0724 \\ THC & 0.066 & 0.057 & 0.141 & 0.078 & 0 & 0.066 & 0.042 & 0.3555 \\ Porosity & 0.000 & \(-0.010\) & 0.075 & 0.012 & \(-0.066\) & 0 & \(-0.025\) & 0.1139 \\ NWA & 0.024 & 0.015 & 0.099 & 0.037 & \(-0.042\) & 0.025 & 0 & 0.1930 \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Judgement matrix. \[M_{Equ}=0.917*M_{Luobe}+0.423*\ M_{Zhiluo}\ +0.076*M_{Yaman} \tag{10}\]  
\[M_{Equ}-\text{{{Equivalent}}}\ \text{thickness}\ \text{of}\ sandstone\]