Coal-Mine Water-Hazard Risk Evaluation Based on the Combination of Extension Theory, Game Theory, and Dempster–Shafer Evidence Theory

Due to the complex hydrogeological conditions and water hazards in coal mines, there are multiple indexes, complexities, incompatibilities, and uncertainty issues in the risk evaluation process of coal-mine water hazards. To accurately evaluate the risk of coal-mine water hazards, a comprehensive evaluation method based on extension theory, game theory, and Dempster–Shafer (DS) evidence theory is proposed. Firstly, a hierarchical water-hazard risk-evaluation index system is established, and then matter-element theory in extension theory is used to establish a matter-element model for coal-mine water-hazard risk. The membership relationship between various evaluation indexes and risk grades of coal-mine water-hazard risk is quantified using correlation functions of extension set theory, and the quantitative results are normalized to obtain basic belief assignments (BBAs) of risk grades for each index. Then, the subjective weights of evaluation indexes are calculated using the order relation analysis (G1) method, and the objective weights of evaluation indexes are calculated using the entropy weight (EW) method. The improved combination weighting method of game theory (ICWMGT) is introduced to determine the combination weight of each evaluation index, which is used to correct the BBAs of risk grades for each index. Finally, the fusion of DS evidence theory based on matrix analysis is used to fuse BBAs, and the rating with the highest belief fusion result is taken as the final evaluation result. The evaluation model was applied to the water-hazard risk evaluation of Sangbei Coal Mine, the evaluation result was of II grade water-hazard risk, and it was in line with the actual engineering situation. The evaluation result was compared with the evaluation results of three methods, namely the expert scoring method, the fuzzy comprehensive evaluation method, and the extension method. The scientificity and reliability of the method adopted in this paper were verified through this method. At the same time, based on the evaluation results, in-depth data mining was conducted on the risk indexes of coal-mine water hazards, and it was mainly found that 11 secondary indexes are the focus of coal-mine water-hazard risk prevention and control, among which seven indexes are the primary starting point for coal-mine water-hazard risk prevention and control. The groundwater index in particular has the most prominent impact. These results can provide a theoretical basis and scientific guidance for the specific water-hazard prevention and control work of coal mines.