# A Status Evaluation of Rock Instability in Metal Mines Based on the SPA-IAHP-PCN Model
## 1 Introduction  
Mineral resources including metal ore and non-metal ore are an important material basis for the development of society and the construction of national economic buildings in the whole world [1]. Globally, the depth of metal mining operations continues to increase, with South Africa and Canada standing out as prominent examples. In China, a significant number of mines have also transitioned to deep mining stages [2]. Many metal mines, therefore, have been put into production in the high-alpine and high-altitude areas in recent years, which makes a significant contribution to China's economic development. However, with the continuous deepening of the mining process and the worsening of the mining environment, the risk of rock instability in metal mines is constantly increasing, making the safe production of metal mines increasingly complex and unpredictable, which in turn leads to rock instability [3]. Rock instability results in substantial harm and significant economic losses, establishing it as one of the primary hazards in metal mining [4]. The accurate evaluation and prediction of rock instability risks in metal mines are crucial for ensuringoperational safety, minimizing economic losses, and preventing potential disasters. Such efforts play a pivotal role in enhancing the sustainability and efficiency of mining activities. Conducting a status evaluation during the production process of enterprises is very important, as it allows for the timely detection of changes in production status. Therefore, many evaluation methods are employed to conduct a status evaluation. These include a Bayesian network [5, 6], game theory [7], grey theory [8, 9], fuzzy mathematic theory [10, 11] evidential reasoning [12, 13], and so on. Moreover, set pair analysis (SPA), put forward by Chinese scholar [PERSON] [14], is also an important analysis method. Because of the characteristics of dealing with certainty and uncertainty issues, SPA is widely employed in the field of status evaluation. [PERSON] et al. [15] proposed a highly efficient deep-learning framework for evaluating wildfire events in the United States and predicting their potential causes and scale. [PERSON] et al. [13] took advantage of SPA to analyze the inner insulation condition of power transformers to obtain the internal insulation state of the transformer. In view of evaluating the complexity and uncertainty of these parameters, the theory of fuzzy set pair analysis was adopted to make a systematic status evaluation of a power transformer by [PERSON] et al. [16]. In a study by [PERSON] [17], the operating status of a wind turbine generator unit was evaluated by utilizing the SPA theory and evidential reasoning. [PERSON] et al. proposed a reliability-based inverse analysis method for determining the shear strength parameters of landslides, addressing the randomness, uncertainty, and nonlinearity inherent in the geotechnical materials, based on the nonlinear Mohr-Coulomb failure criterion [18]. In addition, SPA is not only used to assess the status of equipment but also the urban ecosystem health status [19], river ecosystem status [20, 21] and land ecological security status [22]. So far, the SPA theory has been widely applied in the field of status evaluation. Moreover, this theory is utilized in other fields, for example, the hazard assessment of biomass gasification stations [23], the evaluation of surrounding rock stability [24], flood risk assessment [25], risk assessment of water pollution sources [26], risk assessment of water inrush in karst tunnels [27], and the occupational hazard of coal mining [28]. The IAHP method has further reduced the subjectivity inherent in expert judgment based on AHP; however, subjectivity remains a concern. To minimize this influence further and obtain more objective risk assessment results for metal ones, an IAHP-SPA model is proposed in this study to perform a comprehensive evaluation of rock instability in metal mines.