## 3 Goal Stability Evaluation Based on the Cloud Matter-Element Model  
### Construction of the Cloud Matter-Element Model Based on AHP  
Figure 8 shows that to evaluate the stability of a goaf, first, a stability evaluation indicator system must be built, the classification standard and weight of each indicator must be determined, a cloud matter-element model must be established, and the stability level of the goaf must be calculated. The weighting method in this paper is AHP, which is a subjective weighting method based on the experience of decision makers, a practical multicriteria decision-making method, and a comprehensive evaluation method combining qualitative and quantitative methods [32; 33; 34]. The weights obtained are used in the calculation of the cloud matter-element model. In this study, we invited two experienced professors to participate in the weighting process of the AHP and assign scores to the indicators. \begin{table}
\begin{tabular}{c c c} \hline
\begin{tabular}{c} CSJ-2\#, CSJ-4\#, CSJ-5\#, CSJ-8\#, \\ CSJ-11\#, CSJ-12\#, CSJ-X\#, \\ XJ-4\#, XJ-40\#, NCB-17\# \\ \end{tabular} \\ \hline \end{tabular}
\end{table} 
Table 4: Stability rating of each goaf. \begin{table}
\begin{tabular}{c c c} \hline
**Goaf Stability Level** & **Number of Goafs** & **Goaf Characteristics** \\ \hline \multirow{4}{*}{I} & 10 & The goaf roof displacement is small, the goaf is relatively independent, and the distance from other goafs is far, the plastic zone of surrounding rock is less, the stress is less, and the distance from illegal goafs is far. \\  & 14 & The goaf roof displacement is large, and the distance between the goaf and the surrounding goafs is relatively close, but the goaf density in the area is small, the surrounding rock plastic zone is more, and the roof or pillar area is connected with other goaf plastic zones. The stress state of the roof is close to the tensile stress zone, and the pillar stress is larger. \\  & 10 & The goaf roof displacement is large, the stress state of the roof is poor, local tensile stress occurs, the goaf density in the area is large, the interaction between the goaf, the plastic zone of surrounding rock, and pillar is huge, and a large area of horizontal diffusion and penetration occurs, and it is greatly affected by illegal goafs. The cloud matter-element model is a combination of cloud model and matter-element theory. Matter-element analysis mainly uses the three elements of the thing, name \(J\), feature \(K\), and the corresponding quantity value \(L\), to express things in the form of ordered triples. This triplet is called matter-element and is denoted as \(R=(J,K,L)\). The cloud matter-element model uses the digital features of the cloud model to replace the feature quantity value \(L\) to build the cloud compound element model [35], as shown in Equation (1). \[R=(J,K,L)= \begin{pmatrix}J&K_{1}&(E_{x_{1}},E_{n_{1}},H_{e_{1}})\\ K_{2}&(E_{x_{2}},E_{n_{2}},H_{e_{2}})\\ \vdots&\vdots\\ K_{n}&(E_{x_{n}},E_{x_{n}},H_{e_{n}})\end{pmatrix}  \tag{1}\]  
\(E_{x}\) is the expected value, which is the central value at the center of the domain. \(E_{n}\) is the entropy, which is a measure of the ambiguity of qualitative concepts, and represents the range of all possible values in the discourse domain. The larger the entropy is, the larger the range is, and the stronger the fuzziness is. \(H_{e}\) is the entropy of \(E_{n}\), which represents the dispersion degree of cloud droplets in the cloud model and indirectly reflects the thickness of the cloud. \[E_{x}=\frac{d_{\text{min}}+d_{\text{max}}}{2} \tag{2}\]  
\[E_{n}=\frac{d_{\text{max}}-d_{\text{min}}}{6} \tag{3}\]  
\[H_{e}=k \tag{4}\]  
\(d_{max}\) and \(d_{min}\) are the maximum and minimum values of the value range of evaluation indicators, respectively. \(k\) is a constant, which is determined according to the fuzziness and randomness of the evaluation of goaf stability. In this paper, 0.02 is adopted [18].