The task of smog control in China is still arduous compared with developed economies. To address the problems associated with the uncertain of smog pollution, this paper establishes a new EGM (even grey model) (1,1) prediction model based on the kernel and degree of greyness under the condition that the possibility function is known. The original EGM(1,1) prediction model based on the interval grey number sequence is constructed under circumstances where the possibility function is unknown. For testing the proposed model, the daily AQI data of Nanjing, Jiangsu Province, China, was selected. Also, this paper uses another five forecasting models and compares the results with the new model. The results show that the daily AQI index of Nanjing presents a significant downward trend excluding seasonal factors, and the prediction accuracy of the new EGM (1,1) model is also higher than that of other forecasting models.

The current study proposed the improved non-linear multi-variable Grey Bernoulli model and predicted the CO2 emissions in China. Firstly, the paper presents an improved multivariate grey Bernoulli model (INGBM(1, N)) that considers the nonlinearities of the system characteristic data and related factors in establishing the grey model. Secondly, the influence of the relevant factors on the grey model's forecast accuracy has been considered. The more the number of relevant factors, the higher the relative level with the system characteristic data, the higher the calculation accuracy. However, predictive accuracy began to decrease again after the number of relevant factors more than a specific value. Thirdly, we selected the number of relevant factors as 4 (coal energy consumption, urbanization rate, crude oil, population) and carried out compared analysis with other grey models and non-grey models. The results show that the proposed model has the best forecasting accuracy. The proposed model is a generalization of several other grey forecasting models. China's CO2 emissions for 2019-2021 is forecasted. It estimated that the value would continue to increase over the next three years and reach 9958.57Mt by 2021. Finally, several measures have briefly mentioned reducing CO2 emissions based on the influence of relevant factors.

With the increase of global trade and sourcing, there is a growing need for exact measurement and reliable standards for products and services. This paper attempts to develop a unified and integrated structure for the effectiveness evaluation of quality infrastructure on the promotion of export quality from the perspective of system and coordination. Starting from determining component-based evaluation criteria and index, we propose a three-phase analytical framework. Firstly, the development level of quality infrastructure system is evaluated through factor analysis. Secondly, the coordination degree of quality infrastructure system is calculated by grey coordination evaluation model. Thirdly, we explored the relevance of quality infrastructure system within export quality through grey relational analysis. Using a sample of quality infrastructure and export data from 2009 to 2018 in China, empirical results show that quality infrastructure can be divided into two subsystems according to their characteristics including 'scale and structure subsystem' and 'standard subsystem'. There is evidence that the performance of a quality infrastructure system and its coordination degree are closely related to the upgrade of export product quality. The main contribution of this paper is to address the gap in the quality infrastructure literature by proposing a three-phase analytical framework for effectiveness quantification problems. The clarification of the economic connection between quality infrastructure and export product quality can raise awareness of governments and enterprises about the significance of construction and utilization of quality infrastructure system for competitive advantages.

Studying the development tendency of topics is an important part of the online social network (OSN) analysis. To solve the problems of ad hoc topic popularity, tendency prediction under insufficient samples, data sparsity and low accuracy of the prediction model, this study combines grey system theory with the neural network method to propose a new model for topic tendency prediction. In this study, the grey relational analysis method is used to construct the social network topic popularity evaluation index system, and the topic popularity tendency is classified and weighted based on the grey proximity, and then the integrated system combining GM(1,1) model with BP neural network (BP-NN) model is established. Taking Sina Weibo's bursty topic data as an example, the proposed model's effectiveness is verified. The experimental results show that the proposed hybrid methodology is better than a single independent prediction model and can be effectively used to predict the popularity of a social network topic.

Multi-criteria Decision Aiding (MCDA) paradigm has been utilized in solving classification problems. In this study, a novel MCDA classification method using case-based grey relational analysis (GRA) is proposed to solve the problem of classifying and diagnosing thyroid nodules. After a set of appropriate criteria are identified and qualified, representative cases are selected as input. Weighted distance based on GRA is defined to express the decision maker's preference. Then a quadratic optimization program is constructed to obtain optimal classification thresholds. This method can overcome the difficulties in the clinical diagnosis of thyroid nodules caused by the decision-maker's (DM) cognitive limitations. An experiment is conducted to demonstrate the procedure.

In group decision-making, the behavior expectation of the relevant experts has a significant impact on the selection result of the group decision-making. To address this challenge, a grey target group decision-making model based on expert's expectations was proposed. The article considers the expert's expectations based on the distance between the expert's expected interval of each index and the average (bull's-eye), and the expert weights are derived from their expected interval. The value matrix is then normalized for the degree of interval coincidence between the expert's evaluations and his/her expected interval for the index. Finally, the paper proves the validity and feasibility of the proposed method through a case comparison analysis.

In this study, a GM(1,1)-RV model is proposed to forecast the realized volatility. The heterogeneity of investor with different time horizons is taken into account. Unlike previous studies that used linear regression models, GM(1,1) is employed to model weekly or monthly realized volatility trend based on only 5 or 22 data. The empirical results based on Chinese stock market are demonstrated that the GM(1,1)-RV model can generate better forecasting performance than widely used HAR-RV-type regression models from statistical viewpoint and economic perspectives.

In the area where the temperature changes dramatically, the concrete pavement is affected by high and low temperature for a long time, which changes its internal pore structure and finally leads to the decline of the concrete mechanical properties. Many scholars have studied the relationship between strength and porosity of concrete. Nevertheless, for conclusive findings, a large amount of experimental data is required; otherwise, it is challenging to draw reliable statistical conclusions. For concrete, the properties of raw materials, the production technology, the measuring process of strength and the accuracy of equipment are all uncertain. Multiple uncertainty factors not only contribute to an insufficient amount of experimental data but also inaccuracy. In the current study, in the light of small data samples, the model of total porosity and bending strength of concrete is established based on grey system theory. When compared with other models, it reports a lesser error. By studying the interactions among the pore sizes and the influence on the bending strength, the model is further improved. The average relative error is only 1.63%. The proposed methodology provides an analytical basis for the study of the relationship between pore porosity and bending strength of pavement concrete under temperature fatigue in the area with a large temperature difference. It also provides a specific reference for establishing the relationship model between variables in the case of a small amount of data

Variable selection is the basis of GM(1,N) model, and also one of the key factors that affect grey model performance. Based on the adaptability between actual data and theoretical model, this paper recognizes the parameter estimation of grey model as a general linear model and discusses the effect of variable selection on parameter estimation and prediction performance. It is proved that discarding those relevant variables which have little influence is helpful to improve the modeling accuracy. Then, a variable selection method for GM(1,N) model under RMS, R2 and AIC criteria is proposed, and the calculation order and calculation method are given. Finally, the method is applied to predict the agricultural drought vulnerability in Xinyang City, Henan Province. The results show that the method not only identifies the main influencing factors of drought vulnerability but also further improves the prediction accuracy

Grey prediction theory is an important part of grey system theory. As one of the important models of grey prediction theory, GM (1,1) model has been widely used in economy, management, energy and other fields. In order to improve the prediction accuracy of the classical GM (1,1) model, this paper proposes a combined optimization method, that is, the difference equation is used to replace the static equation in the classical model, and the variable weight is used to construct the background value to reduce the system error caused by human intervention. Taking the domestic soybean annual consumption data as an example, the validity of the combined model is verified. The results show that the prediction accuracy of the combined optimization model is significantly better than that of the classical GM (1,1) model.