## 2 Literature Review
### Grey Fuzzy Comprehensive Evaluation Method Review  
GRA is a method used to identify and evaluate the degree of correlation between internal factors within a system and is a part of grey system theory. This theory is mainly applicable to problems with incomplete or uncertain information, especially in situations where data are limited or information is incomplete. GRA has advantages in testing the degree of interaction and correlation between variables [32]. By comparing the similarities between sequences, it can analyze the relationships between factors, thereby helping decision-makers identify key elements or risk points [33]. In addition, GRA can help solve problems in prediction [34], providing a scientific basis for risk management and decision-making. Compared to other complex statistical analysis methods, the steps involved in GRA are relatively simple, making it easy to understand and execute.  
The core concept of FCE is to allow partial authenticity of phenomena. This method is more in line with human cognitive patterns and the inherent ambiguity of natural language [35]. Fuzzy theory demonstrates flexibility and applicability in the evaluation of complex systems. Through fuzzy methods, hazards can be classified into different risk levels [36]. It is now widely used in various fields, including control systems [37], decision support systems [38], financial analysis [39], and security risk assessment [40], which is the focus of this article. It provides an effective method for managing imprecise information, vague concepts, and uncertain decisions in these fields.  
In order to achieve the risk level of the equipment, FCE integrates fuzzy assessments of different standards using risk weights from risk analysis. Then integrate these impactsinto the overall evaluation and ranking [41]. This improves the accuracy and reliability of the overall evaluation. [PERSON] et al. [42] applied this method to evaluate the tourist satisfaction of free parks in Xi'an. They identified important factors that affect satisfaction and discussed strategies for park development based on these findings. [PERSON] and [PERSON] [43] used the Analytic Hierarchy Process to allocate weights to evaluation indicators and then used FCE to evaluate the potential for the development of forest health tourism. This provides a new perspective and practical support for the development of the industry. [PERSON] et al. [44] established a construction project safety evaluation index system based on key factors affecting construction safety and a fuzzy comprehensive safety evaluation model. They evaluated the safety status of the construction project based on the principle of maximum membership. These studies indicate that FCE is an effective tool for addressing uncertainty and subjectivity in security risk assessment. Its correct application can improve the scientific rigor of risk assessment and the rationality of decision-making. However, in order to make the results obtained by the fuzzy comprehensive evaluation method professional and reliable, research requires a large amount of expert knowledge and practical data support.  
Considering the advantages and disadvantages of the above methods, the grey fuzzy comprehensive evaluation method proposed in this article can effectively compensate for the shortcomings of the two methods and solve the problem of lack of data for performing arts equipment. Analyzing the importance of different risk factors through methods provides a scientific basis for risk management. Meanwhile, the method proposed in this article can comprehensively consider multiple factors and standards and effectively handle uncertain and ambiguous information in the evaluation process. Through the evaluation of professionals, the risk level of different types of performance accidents in stage suspension equipment can be obtained, achieving a comprehensive safety risk assessment of in-service stage suspension equipment.