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The purpose of this paper is to study the properties of derived grey verhulst prediction model with multiplication transformation and reduce its modeling complexity.

The paper discussed the parameter characteristics of grey derived verhulst model under multiple transformation, and demonstrated its effect on its simulative value and predictive value by investigating the multiple transformation acting on the raw data sequence of this grey model. The parameter characteristics of this model under multiple transformations and its effect of the simulation value and forecasting value are analyzed by studying the properties of multiply transformation of this model.

The research finding shows that the modeling accuracy of derived grey verhulst model is in no relation to multiple transformations.

The above results imply that the data level can be reduced; the process of building derived grey verhulst model can be simplified; but the simulative and predictive accuracy of this model remain unchanged.

The paper succeeds in realising the properties of derived grey verhulst model by using the method of multiplication transformation, which is helpful to understand the modeling mechanism and expand the application range of derived grey verhulst model.

The purpose of this paper is to propose a novel approach to improve prediction accuracy of grey power models including GM(1, 1) and grey Verhulst model.

The modified new models are proposed by optimizing the initial condition and model parameters. The new initial condition consists of the first item and the last item of a sequence generated by applying the first-order accumulative generation operator on the sequence of raw data.

It is shown that the newly modified grey power model is an extension of the previous optimized GM(1, 1) and grey Verhulst model. And the optimized initial condition reflected the principle of new information priority.

The result of a numerical example indicates that the modified grey model presented in this paper with better prediction performance.

The new initial condition are derived by weighted combination of the first item and the last item. The coefficients of weight obtained by the least square method.

The purpose of this paper is to build a linear time-varying discrete Verhulst model (LTDVM), to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations.

The methodology of the paper is by the light of discrete thoughts and countdown to the original data sequence.

The research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.

The example analysis shows that LTDVM embodies simulation and prediction with high precision.

This paper is to realise the convert from continuous forms to discrete forms, and to eliminate traditional grey Verhulst model's error caused by difference equations directly jumping to differential equations. Meanwhile, the research of this model manifests that LTDVM is unbiased on the “s” sequential simulation.

In order to accurately predict the uncertain and nonlinear characteristics of China's three clean energy generation, this paper presents a novel time-varying grey Riccati model (TGRM(1,1)) based on interval grey number sequences.

By combining grey Verhulst model and a special kind of Riccati equation and introducing a time-varying parameter and random disturbance term the authors advance a TGRM(1,1) based on interval grey number sequences. Additionally, interval grey number sequences are converted into middle value sequences and trapezoid area sequences by using geometric characteristics. Then the predicted formula is obtained by using differential equation principle. Finally, the proposed model's predictive effect is evaluated by three numerical examples of China's clean energy generation.

Based on the interval grey number sequences, the TGRM(1,1) is applied to predict the development trend of China's wind power generation, China's hydropower generation and China's nuclear power generation, respectively, to verify the effectiveness of the novel model. The results show that the proposed model has better simulated and predicted performance than compared models.

Due to the uncertain information and continuous changing of clean energy generation in the past decade, interval grey number sequences are introduced to characterize full information of the annual clean energy generation data. And the novel TGRM(1,1) is applied to predict upper and lower bound values of China's clean energy generation, which is significant to give directions for energy policy improvements and modifications.

The main contribution of this paper is to propose a novel TGRM(1,1) based on interval grey number sequences, which considers the changes of parameters over time by introducing a time-varying parameter and random disturbance term. In addition, the model introduces the Riccati equation into classic Verhulst, which has higher practicability and prediction accuracy.

In recent years, continuous expansion of the scale of the new energy export industry in China caused a boycott of American and European countries. Export injury early warning research is an urgent task to develop the new energy industry in China. The purpose of this paper is to build an indicator system of exports injury early warning of the new energy industry in China and corresponding quantitative early warning models.

In consideration of the actual condition of the new energy industry in China, this paper establishes an indicator system according to four aspects: export price, export quantity, impact on domestic industry and impact on macro economy. Based on the actual data of new energy industry and its five sub-industries (solar, wind, nuclear power, smart grid and biomass) in China from 2003 to 2013, GM (1,1) model is used to predict early warning index values for 2014-2018. Then, the principal component analysis (PCA) is used to obtain the comprehensive early warning index values for 2003-2018. The 3-sigma principle is used to divide the early warning intervals according to the comprehensive early warning index values for 2003-2018 and their standard deviation. Finally, this paper determines alarm degrees for 2003-2018.

Overall export condition of the new energy industry in China is a process from cold to normal in 2003-2013, and the forecast result shows that it will be normal from 2014 to 2018. The export condition of the solar energy industry experienced a warming process, tended to be normal, and the forecast result shows that it will also be normal in 2014-2018. The biomass and other new energy industries and nuclear power industry show a similar development process. Export condition of the wind energy industry is relatively unstable, and it will be partially hot in 2014-2018, according to the forecast result. As for the smart grid industry, the overall export condition of it is normal, but it is also unstable, in few years it will be partially hot or partially cold. The forecast result shows that in 2014-2018, it will maintain the normal state. In general, there is a rapid progress in the export competitiveness of the new energy industry in China in the recent decade.

Export injury early warning research of the new energy industry can help new energy companies to take appropriate measures to reduce trade losses in advance. It can also help the relevant government departments to adjust industrial policies and optimize the new energy industry structure.

This paper constructs an index system that can measure the alarm degrees of the new energy industry. By combining the GM (1,1) model and the PCA method, the problem of warning condition detection under small sample data sets is solved.

The purpose of this paper is to provide a modeling approach using grey power model with first‐order one‐variable (abbreviated as GPM(1,1)) for forecasting small sample oscillating series.

An optimization method is used to determine the initial value in GPM(1,1) model, and furthermore, the power value in the model is optimized by utilizing a non‐linear programming model. An operations research software LINGO is employed to solve the non‐linear optimization model.

The results show that the optimized GPM(1,1) model can flexibly adjust the parameters to make the forecasting results more in line with the actual data; therefore, for a given small sample oscillating series, if an appropriate way to find the optimal parameters is taken, accurate predictions should be obtained.

The modeling approach proposed in the paper can be used to forecast new product sales, new industry development trend, equipment remaining life, disaster emergency material demand, etc.

The paper extends the application range of the grey model for forecasting small sample oscillating series by using grey power model GPM(1,1).

Research on grey systems is becoming more sophisticated, and grey relational and prediction analyses are receiving close review worldwide. Particularly, the application of grey systems in marine economics is gaining importance. The purpose of this paper is to summarize and review literature on grey models, providing new directions in their application in the marine economy.

This paper organized seminal studies on grey systems published by Chinese core journal database – CNKI, Web of Science and Elsevier from 1982 to 2018. After searching the aforementioned database for the said duration, the authors used the CiteSpace visualization tools to analyze them.

The authors sorted the studies according to their countries/regions, institutions, keywords and categories using the CiteSpace tool; analyzed current research characteristics on grey models; and discussed their possible applications in marine businesses, economy, scientific research and education, marine environment and disasters. Finally, the authors pointed out the development trend of grey models.

Although researches are combining grey theory with fractals, neural networks, fuzzy theory and other methods, the applications, in terms of scope, have still not met the demand. With the increasingly in-depth research in marine economics and management, international marine economic research has entered a new period of development. Grey theory will certainly attract scholars’ attention, and its role in marine economy and management will gain considerable significance.

The purpose of this paper is to present the terms of grey forecasting models and techniques.

The definitions of basic terms about grey forecasting models and techniques are presented one by one.

The reader could know the basic explanation about the important terms about various grey forecasting models and techniques from this paper.

Many of the authors’ colleagues thought that unified definitions of key terms would be beneficial for both the readers and the authors.

It is a fundamental work to standardise all the definitions of terms for a new discipline. It is also propitious to spread and universal of grey system theory.

The purpose of this paper is to summarize progress of grey forecasting modelling, explain mechanism of grey forecasting modelling and classify exist grey forecasting models.

General modelling process and mechanism of grey forecasting modelling is summarized and classification of grey forecasting models is done according to their differential equation structure. Grey forecasting models with linear structure are divided into continuous single variable grey forecasting models, discrete single variable grey forecasting models, continuous multiple variable grey forecasting models and discrete multiple variable grey forecasting models. The mechanism and traceability of these models are discussed. In addition, grey forecasting models with nonlinear structure, grey forecasting models with grey number sequences and grey forecasting models with multi-input and multi-output variables are further discussed.

It is clearly to explain differences between grey forecasting models with other forecasting models. Accumulation generation operation is the main difference between grey forecasting models and other models, and it is helpful to mining system developing law with limited data. A great majority of grey forecasting models are linear structure while grey forecasting models with nonlinear structure should be further studied.

Mechanism and classification of grey forecasting models are very helpful to combine with suitable real applications.

The main contributions of this paper are to classify models according to models' structure are linear or nonlinear, to analyse relationships and differences of models in same class and to deconstruct mechanism of grey forecasting models.