# Rockburst Hazard Evaluation Using an Extended COPRAS Method with Interval-Valued Fuzzy Information
###### Abstract  
Rockburst is a major disaster in deep mining engineering, which can cause serious injury, death and economic losses. This study aims to solve rockburst hazard evaluation problems and determine the hazard levels of mines under uncertain circumstances. To this end, a novel multicriteria decision-making (MCDM) method was proposed in an interval-valued fuzzy context. The main contributions are three-fold. First, considering the heterogeneity of rock masses and the complexity of mining engineering, interval-valued fuzzy numbers (IVFNs) were adopted to express initial indicator information. Second, accounting for the uncertainty of indicator weights, the decision-making trial and evaluation laboratory (DEMATEL) and entropy methods were extended with IVFNs to determine fuzzy indicator weights comprehensively. Third, the complex proportional assessment (COPRAS) approach was extended with IVFNs to determine the rockburst hazard level. Finally, the proposed method was applied to evaluate rockburst hazards in the Jiaojia gold mine, and the ranking results were consistent with field status. Meanwhile, sensitivity and comparison analyses were performed to reveal the stability and effectiveness of the proposed method. The results indicated that the extended COPRAS method was reliable for rockburst hazard evaluation in deep mining engineering. rockburst; hazard evaluation; multicriteria decision making; uncertainty;  
energy-based, brittleness-based, strength-based and stiffness-based criteria. The typical criteria include the peak elastic strain energy index [11], coefficient of deformation for brittleness [12], the geological strength index [13], the roof-pillar stiffness ratio [14] and so on [15; 16]. Because of their simplicity and efficiency, the empirical criteria are widely used in practical engineering. However, only using a single criterion is insufficient to tackle the complexity of rockbursts. Due to the progress in rock mechanics and computational science, numerical simulation methods have become effective methods for rockburst hazard evaluation. Many prominent types of simulation software have been applied for rockburst hazard analysis, such as fast Lagrangian analysis of continua [17], realistic failure process analysis [18], particle flow code [19] and so on [20; 21]. Many indicators have been proposed for the simulation of rockbursts, including the absolute local energy release rate [22], energy dissipation rate [23], burst potential index [24] and so on [25; 26]. The numerical simulation method can consider the effects of in situ stress, rock parameters and excavation activities simultaneously. However, it is difficult to precisely determine the input and constitutive relationship of the model. Recently, various mathematical algorithms have been developed to evaluate rockburst hazards, and these algorithms can be classified into three types. The first one is the machine learning algorithm. Many machine learning algorithms have been applied to analyze rockburst hazards, such as decision trees [27], ensemble learning [28] and artificial neural networks [29]. Machine learning algorithms can build a complex and nonlinear relationship between indicators and hazard levels based on existing rockburst cases. However, the accuracy of this kind of methodology can only be ensured by using large amounts of reliable data. The second one is the uncertainty method. Typical approaches include extensible comprehensive evaluation [30], unascertained measure theory [31], the fuzzy comprehensive assessment method [32] and so on [33; 34]. These methods can characterize the uncertainties of rockburst hazards by using membership functions. However, the reliable membership functions are difficult to determine. The third one is the multicriteria decision-making method (MCDM), which not only can simultaneously consider multiple indicators, but can also deal with uncertainties by coupling with fuzzy theory [35; 36]. For example, [PERSON] et al.