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.

Recognizing that the evaluation of the overseas petroleum investment environment is affected by many uncertain factors and that there are problems with current evaluation methods, this paper proposes a mathematical evaluation model of an overseas oil resources investment environment, based on a combination of the weighting and uncertainty measure theory. Combining international investment environment theory with the characteristics of the petroleum industry, this paper establishes an evaluation index system for the overseas petroleum investment environment and the linear uncertainty measure function of each index. Using the subjective weight obtained using an analytic hierarchy process together with the objective weight obtained using the entropy weight method, the optimal weight of each evaluation index was obtained using minimum relative information entropy. A multi-index evaluation matrix of the top 12 oil-producing countries in Africa was calculated. Finally, the credible degree recognition criterion was used to judge the order and level of the oil investment environment. This model provides an effective method for the evaluation of the overseas petroleum investment environment. The results show that Nigeria and Angola have the best investment climate, followed by Algeria, Egypt, and Libya. In general, Africa is an important strategic partner of China and is rich in oil resources. Although Africa’s oil industry is fraught with complex challenges and headwinds, challenges also present opportunities.

The prediction of possibility and risk classification of collapse is an important issue in the process of highway construction in mountain area. Based on the principle of rough set and support vector machine, a landslide hazard prediction model was established. First of all, according to field investigation, an evaluation index system and a sample set of evaluation index data were established, the rough set decision table was constructed by preprocessing the original data based on the function classification of standard evaluation index, and then, the influence indexes of the collapse activity were reduced by rough set theory, and the main 9 indexes affecting the collapse activity as the key discriminant factors of support vector machine model, namely slope shape of slope, aspect of slope, slope of slope, height of slope, exposed structural face, stratum lithology, relationship between weakness face and free face, vegetation cover rate and weathering degree of rock were extracted. Then, taking the data of 13 post earthquake collapses in Yingxiu-Wolong highway of Hanchuan County measured by the authors in the field as training samples, the optimal model parameters were analyzed and calculated. When the penalty parameter $$C$$ C is 8 and the kernel parameter $$\sigma$$ σ is 0.5, the correct rate of cross-validation is 100%, and the model is optimal. At last, 4 other landslide data were tested, the discriminant results of the test sample data were compared with the results obtained by uncertainty measure and distance discriminant analysis. The results show that the discriminant results of the test sample data by RS-SVM were consistent with the results obtained by uncertainty measure and distance discriminant analysis, the accurate rate is 100%. The collapse hazard analysis model based on rough set and support vector machine can reduce the computation while ensuring the accuracy of evaluation, and better solve the small sample and nonlinear problems, can provide certain a good idea for collapse hazard evaluation in the future.