Because of the harmful influence of CO₂ emissions on the environment and humans, issues related to CO₂ emissions have received considerable attention in recent years. Based on the pollution haven hypothesis and pollution halo effect, the uncertain effect of bilateral foreign direct investment (FDI) on CO₂ emissions has recently been in focus. Moreover, because of the opposing capital flow of bilateral FDI, the interaction between inward FDI (IFDI) and outward FDI (OFDI) might have a trade-off effect on CO₂ emissions. The accurate forecasting of CO₂ emissions in China in light of effect of the bilateral FDI is important since the government can use it to regulate emissions’ reduction. The grey multivariable Verhulst model (GMVM) was formulated in this paper with the goal of forecasting CO₂ emissions in China by considering the nonlinear, independent, and interaction-related effects of bilateral FDI on them. To enhance the accuracy of prediction, this paper used the Fourier series and the grey prediction model for residual modifications. The empirical results showed that the IFDI and the item of the interaction of bilateral FDI promoted CO₂ emissions, whereas OFDI reduced them in China. These results also verified the higher precision of the improved GMVM relative to other models. This paper also used improved GMVM to further forecast CO₂ emissions and provided suggestions for the Chinese government to plan for foreign investment, including selectively implementing bilateral FDI, and focusing on the trade-off in its interaction-related effects.

As a crucial part of producer services, the logistics industry is highly dependent on the manufacturing industry. In general, the interactive development of the logistics and manufacturing industries is essential. Due to the existence of a certain degree of interdependence between any two factors, interaction between the two industries has produced a basis for measurement; identifying the key factors affecting the interaction between the manufacturing and logistics industries is a kind of decision problem in the field of multiple criteria decision making (MCDM). A hybrid MCDM method, DEMATEL-based ANP (DANP) is appropriate to solve this problem. However, DANP uses a direct influence matrix, which involves pairwise comparisons that may be more or less influenced by the respondents. Therefore, we propose a decision model, Grey DANP, which can automatically generate the direct influence matrix. Statistical data for the logistics and manufacturing industries in the China Statistical Yearbook (2006–2015) were used to identify the key factors for interaction between these two industries. The results showed that the key logistics criteria for interaction development are the total number of employees in the transport business, the volume of goods, and the total length of routes. The key manufacturing criteria for interaction development are the gross domestic product and the value added. Therefore, stakeholders should increase the number of employees in the transport industry and freight volumes. Also, the investment in infrastructure should be increased.

Time series data for decision problems such as energy demand forecasting are often derived from uncertain assessments, and do not meet any statistical assumptions. The interval grey number becomes an appropriate representation for an uncertain and imprecise observation. In order to obtain nonlinear interval grey numbers with better forecasting accuracy, this study proposes a combined model by fusing interval grey numbers estimated by neural networks (NNs) and the grey prediction models. The proposed model first uses interval regression analysis using NNs to estimate interval grey numbers for a real valued sequence; and then a grey residual modification model is constructed using the upper and lower wrapping sequences obtained by NNs. It turns out that two different kinds of interval grey numbers can be estimated by nonlinear interval regression analysis. Forecasting accuracy on real data sequences was then examined by the best non-fuzzy performance values of the combined model. The proposed combined model performed well compared with the other interval grey prediction models considered.

Since the implementation of the Belt and Road Initiative, China’s total amount of outward foreign direct investment (OFDI) has increased each year and this has caused its relationship with carbon emissions (CO₂e) to receive great attention recently. Forecasting China’s CO₂e accurately by considering the impact of OFDI is important since the government can use it to formulate an appropriate emissions plan to fulfill its carbon reduction commitments. Because the relationship between OFDI and CO₂e has nonlinear characteristics, a nonlinear grey multivariable model with fractional-order accumulation (NFGM(1,N)) was proposed in this study. To enhance the prediction accuracy, an optimization process was used to determine the parameters. The outcomes of the variable fractional order showed that fractional-order accumulation can better extract the grey information hidden in the original data, which confirmed the principle of new information priority. The result of the power coefficient indicated a nonlinear relationship between the CO₂e and OFDI. Based on the prediction performance, the prediction accuracy of the NFGM(1,N) model was proven to be superior to those of the ARMA model, linear regression model, the GM(1,1), GM(1,N), and FGM(1,N) models. The empirical results also revealed that OFDI increased the CO₂e in China. The relationship between the CO₂e and OFDI exhibits a U-shaped development based on further predictions for the 2018–2030 period. Finally, some suggestions for long-term CO₂e reduction plans were provided in this paper.