Traditional discrete grey forecasting model can effectively predict the development trend of the stabilizing system. However, when the system has disturbance information, the prediction result will have larger error, and there will appear significant downward trend in the stability of the model. In the presence of disturbance information, this paper presents a fractional-order linear time-varying parameters discrete grey forecasting model to deal with the system that contains both linear trend and nonlinear trend. The modeling process of the model and calculation method are given. The perturbation bounds of the new model are analyzed by using the least-squares method of perturbation theory. And it is compared with that of the first-order linear time-varying parameters discrete grey forecasting model. Finally, two real cases are given to verify the effectiveness and practicality of the proposed method.

China’s increasing energy consumption poses challenges to economy and environment. How to predict the energy consumption accurately and regulate the future energy consumption production is a problem worth studying. In this paper, the fractional order cumulative linear time-varying parameter discrete grey prediction model (FTDGM (1, 1) model) is introduced. Firstly, the data are preprocessed by buffer operators, and then, the FTDGM (1, 1) model is established. In this paper, the parameter estimation method and the specific process of model establishment are presented. Finally, the models of energy consumption in China are built. The advantages and prediction accuracy of the model established in this paper are analyzed, and the data in the following years are effectively predicted, so as to provide theoretical support for the government to formulate reasonable energy policies.

Buffer operators can effectively weaken the impact disturbance of the system and restore the original appearance of the system. However, the buffer strength of the existing buffer operator is fixed, and the buffer strength cannot be adjusted. So the buffer effect for the system impact disturbance is not flexible enough, and the accuracy of the prediction model established is not high. In order to solve this problem, this paper proposes weakened buffer operators with time-varying parameters, analyzes the properties of the newly constructed buffer operator, and proves the superiority of the new buffer operators theoretically. Finally, the new buffer operators proposed in this paper are applied to the prediction of the number of employees in China’s air transport industry and the unsafe events in China’s civil aviation. The results show that the proposed buffer operators are better than the existing buffer operators, which further verify the validity and practicability of the proposed buffer operators.

Grey system theory is an effective mathematical method for studying small sample data and solving poor information problems. The grey correlation model and grey prediction model in this theory have been widely used in scientific studies in various industries. Currently, it is quite difficult for China to formulate scientific policies as livestreaming e-commerce is an emerging industry with little available annual data; therefore, the use of grey system theory is crucial to the study of the future scale of livestreaming e-commerce. In this paper, of many factors influencing the development of livestreaming e-commerce, 14 predictors of livestreaming e-commerce development scale were selected to construct a grey correlation model, by which 5 main predictors were determined. Based on the predictors identified above, 4 grey prediction models of GM (1,1), DGM (1,1), NDGM (1,1), and FDGM (1,1) were constructed, and the accuracy of these models was compared. It was concluded that the NDGM (1,1) model had the best simulation effect. The NDGM (1,1) model is then used to forecast and analyse the indicators of livestreaming e-commerce development scale from 2021 to 2023, and some relevant suggestions were made. This paper applies the new modelling approach to livestreaming e-commerce studies, thus broadening the theoretical study field of livestreaming e-commerce. Moreover, the findings can help the Chinese government make more reasonable and effective decisions as a new study on livestreaming e-commerce was conducted from a different perspective in this paper.