Taking into account the limitations of the single weighting method presently used for the environmental risk evaluation of overseas mining investment, an improved extension evaluation method based on game theory was developed. The method was then applied to real data from the Philippines and used to establish the congener element object and classical domain of the environmental risk of mining investment in the Philippines, based on extension matter element theory. The optimal index weights, based on a balance of subjective and objective results, were obtained from game theory, the analytic hierarchy process, and entropy weight theory. This enabled calculation of the association function values of evaluation indexes in the Philippines and the environmental risk level of overseas mining investment. Finally, given the weighting and association function values, the environmental risk level of mining investment in the Philippines was determined to be level II (higher risk). These results show that the proposed model is effective for evaluating the environmental risk of overseas mining investment.

Based on uncertainty measure theory, a stability classification and order-arranging model of surrounding rock was established. Considering the practical engineering geologic condition, 5 factors that influence surrounding rock stability were taken into account and uncertainty measure function was obtained based on the in situ data. In this model, uncertainty influence factors were analyzed quantitatively and qualitatively based on the real situation; the weight of index was given based on information entropy theory; surrounding rock stability level was judged based on credible degree recognition criterion; and surrounding rock was ordered based on order-arranging criterion. Furthermore, this model was employed to evaluate 5 sections surrounding rock in Dongshan tunnel of Huainan. The results show that uncertainty measure method is reasonable and can have significance for surrounding rock stability evaluation in the future.

The prediction and risk classification of collapse is an important issue in the process of highway construction in mountainous regions. Based on the principles of information entropy and Mahalanobis distance discriminant analysis, we have produced a collapse hazard prediction model. We used the entropy measure method to reduce the influence indexes of the collapse activity and extracted the nine main indexes affecting collapse activity as the discriminant factors of the distance discriminant analysis model (i.e., slope shape, aspect, gradient, and height, along with exposure of the structural face, stratum lithology, relationship between weakness face and free face, vegetation cover rate, and degree of rock weathering). We employ postearthquake collapse data in relation to construction of the Yingxiu-Wolong highway, Hanchuan County, China, as training samples for analysis. The results were analyzed using the back substitution estimation method, showing high accuracy and no errors, and were the same as the prediction result of uncertainty measure. Results show that the classification model based on information entropy and distance discriminant analysis achieves the purpose of index optimization and has excellent performance, high prediction accuracy, and a zero false-positive rate. The model can be used as a tool for future evaluation of collapse risk.

The fault fractal dimension is the integrated reflection of the quantity, scale, degree of development, combination mode, and dynamic mechanism of a fault and can be used as a quantitative indicator of fault structure complexity. In Hutouya polymetallic orefield of Qinghai province, China, the faults are developed, and many ore belts are located in the fault zone, which indicated that the faults have an important role in controlling mineralization. The two‐dimensional horizontal distribution of fault systems in the IV, V, VI, and VII ore zones of Hutouya orefield was studied based on fractal geometry. The fault distribution has fractal dimension values for zones IV, V, VI, and VII of 1.05, 1.157, 1.311, and 1.05, respectively. From the perspective of favourable structure, the potential for metallogenesis in the four ore zones is VI > VII > V > IV. The main controlling factor on ore formation in the Qimantage region is fault structure, and the results are consistent with the actual results. This work provides new insights into the relationship between fault systems and metallogenesis.

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Analyzing showed that the safety risk evaluation for CO2geological storage had important significance. Aimed at the characteristics of CO2geological storage safety risk evaluation, drawing on previous research results, rank and order models for safety risk evaluation of CO2geological storage were put forward based on information entropy and uncertainty measure theory. In this model, the uncertainty problems in safety risk evaluation of CO2geological storage were solved by qualitative analysis and quantitative analysis, respectively; uncertainty measurement functions for the relevant factors were established based on experimental data; information entropy theory was applied to calculate the index weight of factors; safety risk level was judged based on credible degree recognition criterion and ordered. This model was applied in three typical zones of Erdos and Hetao basins. The results show that uncertainty measure method is objective and reasonable and can be used as a new way to evaluate the safety of CO2geological storage sites in the future.

In the application of uncertainty measure theory, the determination method of index weight mainly includes the subjective weight determination method and the objective weight determination method. The subjective weight determination method has the disadvantages affected by the subjective preference of the decision-maker. The objective weight determination method often ignores the participation degree of the decision-maker, and when using the uncertainty measure evaluation model to perform multi-index classification evaluation, the credible degree recognition criterion is often used as the attribute recognition of the object to be measured, because the credible degree is taken by the subjective people, and the different values of different people have a great influence on the evaluation results. In order to solve the above problems in the uncertainty measure theory, this paper used the combination weighting of game theory to determine the optimal weight. At the same time, the credible degree recognition criterion was improved on the basis of the concept of minimum uncertainty measure distance, and a game theory-improved uncertainty measure optimization model was proposed. Finally, the validity of the model was proven by a case.

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