# Rockburst Hazard Evaluation Using an Extended COPRAS Method with Interval-Valued Fuzzy Information
###### Abstract
[37] extended the preference ranking organization method for enrichment evaluation (PROMETHEE) with trapezoid fuzzy numbers to assess rockburst hazards. [PERSON] et al. [38] combined the technique for order preference by similarity to an ideal solution (TOPSIS) and rough set theory to evaluate rockburst hazards. [PERSON] et al. [39] extended the multiattributive border approximation area comparison (MABAC) method with triangular fuzzy numbers to assess rockburst hazards. Moreover, a novel MCDM method, the complex proportional assessment (COPRAS) approach, was proposed by [PERSON] et al. [40; 41]. This is an effective method that considers both the positive-ideal and negative-ideal solutions [42]. The benefit- and cost-type indicators are first considered separately, and then combined to determine the significance performance of each sample. Due to the simplicity and flexibility of the COPRAS approach, it has been applied in many fields. For example, [PERSON] et al. [43] applied the COPRAS method to sustainability assessment of the optimal locations of electric vehicle charge stations. [PERSON] et al. [44] used the COPRAS method to select sustainable hydrogen fuel cell suppliers of new energy vehicles. Notably, the indicator values are an important basis for rockburst hazard evaluation. Considering the heterogeneity and anisotropy of rock masses, the indicator values have some uncertainties. For example, one could suppose that the values of unconfined compressive strength are determined as 97 MPa, 105 MPa and 110 MPa, and the average value is 104 MPa. However, if the values are determined as 95 MPa, 103 MPa and 114 MPa, the average value is still 104 MPa. Obviously, the obtained crisp values smooth out the difference. Therefore, crisp numbers are insufficient to fully characterize the indicator information in rockburst evaluation. Fuzzy numbers are capable of considering the uncertainties adequately, and have been successfully applied in different engineering fields [45; 46]. As typical fuzzy numbers, interval-valued fuzzy numbers (IVFNs) are suggested to fully describe the uncertain information. The tangential stress index can be taken as an example. Supposing there are determined values of 0.3, 0.4 and 0.5 for sample one, and 0.35, 0.4 and 0.45 for sample two, they can be represented by two IVFNs, [0.3, 0.5] and [0.35, 0.45]. It is clear that the uncertainties are better considered than the average value of 0.4. Therefore, IVFNs may be a more informative and convenient way to describe indicator values in rockburst evaluation. To the best of our knowledge, IVFNs have not been combined with the COP RAS method for rockburst hazard evaluation. The main purpose of this study is to develop a novel methodology integrating IVFNs with the COPRAS, DEMATEL and entropy methods. The key contributions are summarized as follows: First, IVFNs are adopted to better capture the uncertainties of indicator values. Second, evaluating rockburst hazards with fuzzy indicator weights has rarely been considered in previous studies. The DEMATEL and entropy methods are extended with IVFNs to determine the fuzzy indicator weights. Third, the COPRAS method is extended with IVFNs to evaluate the rockburst hazard. In summary, the rest of this paper is organized as follows. The preliminaries of IVFNs are indicated in the section \"Preliminaries\". The details of the proposed methodology are introduced in the section \"Methodology\". The proposed methodology is adopted to evaluate the rockburst hazard in Jiaojia gold mine in the section \"Case study\". The section \"Discussion\" further demonstrates the stability and effectiveness of the proposed methodology. Finally, the \"Conclusions\" are made.