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The purpose of this paper is to provide a foundational reference and practical guidance for modelling small and poor data with incomplete information.

The definitions of four basic models of GM(1, 1), such as Even Grey Model (EGM), Original Difference Grey Model (ODGM), Even Difference Grey Model (EDGM) and Discrete Grey Model (DGM), are put forward. The properties and characteristics of different models are studied and their equivalence are proved. The suitable sequences of different models are studied by simulation and analysis with homogeneous exponential sequences, nonhomogeneous exponential increasing sequences and vibration sequences.

The main conclusions have been obtained as follows: first, the three discrete models of ODGM, EDGM and DGM are suitable for homogeneous exponential sequences or sequences which close to a homogeneous exponential sequence; and second the EGM are suitable for nonhomogeneous exponential increasing sequences and vibration sequences.

The outcome obtained in this paper can be consulted for model selection in the course of practical modelling.

This paper systematically defined the four basic forms of model GM(1, 1) and studied their properties and characteristics, especially their suitable sequences. Although significant progress has been made in this field, such a systematic study on these models and their suitable sequences is still missing as far as we know. It can provide reference and basis for people to choose the correct model in the actual modelling process.

The purpose of this paper is to present a novel GREY‒ASMAA model for reliability growth evaluation in the large civil aircraft test flight phase.

As limited data are collected during the large civil aircraft test flight phase, which are not enough to meet the requirements of the ASMAA model for reliability growth, four basic GM(1, 1) models, even grey model, original difference grey model, even difference grey model and discrete grey model, are presented. Then both forward and backward grey models GM(1,1) are built to forecast and obtain virtual test data on left and right sides. Then the ASMAA model for reliability growth evaluation can be built based on original and virtual test data.

Aiming at the background of poor information data during the large civil aircraft test flight phase, first, a novel GREY‒ASMAA model, which was combined by the grey model GM(1,1) with the ASMAA model, has been put forward in this paper.

The GREY‒ASMAA model for reliability growth evaluation can be used to solve the problem of reliability growth evaluation with poor information data during the large civil aircraft test flight phase, and it has been used in reliability evaluation of C919 at the test flight stage.

This paper presents two new definitions of forward grey model GM(1,1) and backward grey model GM(1,1), as well as a novel GREY‒ASMAA model for reliability growth evaluation of large civil aircraft during test flight phase.

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 solve the problem of quality prediction in the equipment production process and provide a method to deal with abnormal data and solve the problem of data fluctuation.

The analytic hierarchy process-process failure mode and effect analysis (AHP-PFMEA) structure tree is established based on the analytic hierarchy process (AHP) and process failure mode and effect analysis (PFMEA). Through the failure mode analysis table of the production process, the weight of the failure process and stations is determined, and the ranking of risk failure stations is obtained so as to find out the serious failure process and stations. The spectrum analysis method is used to identify the fault data and judge the “abnormal” value in the fault data. Based on the analysis of the impact, an “offset operator” is designed to eliminate the impact. A new moving average denoise operator is constructed to eliminate the “noise” in the original random fluctuation data. Then, DGM (1,1) model is constructed to predict the production process quality.

It is discovered the “offset operator” can eliminate the impact of specific shocks effectively, moving average denoise operator can eliminate the “noise” in the original random fluctuation data and the practical application of the shown model is very effective for quality predicting in the equipment production process.

The proposed approach can help provide a good guidance and reference for enterprises to strengthen onsite equipment management and product quality management. The application on a real-world case showed that the DGM (1,1) grey discrete model is very effective for quality predicting in the equipment production process.

The offset operators, including an offset operator for a multiplicative effect and an offset operator for an additive effect, are proposed to eliminate the impact of specific shocks, and a new moving average denoise operator is constructed to eliminate the “noise” in the original random fluctuation data. Both the concepts of offset operator and denoise operator with their calculation formulas were first proposed in this paper.

The purpose of this paper is to summarize the advances in grey system theory research and various application achievements in science and engineering. At the same time, it commemorates the 40th anniversary of the birth of grey system theory and the 10th anniversary of Grey Systems–Theory and Application.

Firstly, the innovations of theoretical research in grey system theory were summarized and some of the widely recognized new results are briefly described. By searching and combing the research results of grey system theory in China national knowledge infrastructure (CNKI) database and Web of Science by Institute for Scientific Information (ISI), this paper shows the rapid development trend of grey system theory in the past 40 years, and the successful applications of grey system theory in the fields of social sciences, natural sciences and engineering technologies.

More than 227 thousands literature were found by input 10 phrases such as grey system, grey number and sequence operator etc. in CNKI database. After entering the new century, the number of grey system papers included in CNKI database is increasing rapidly. Since 2008, more than 10 thousands papers have been included per year and more than 15 thousands papers have been included per year since 2014. Grey system method and model are widely used in physics, chemistry, biology and other fields of natural science, as well as transportation, electric power, machinery and other fields of engineering technology, and a large number of valuable results have been achieved.

It can be seen that the grey system theory plays an important role in promoting China’s scientific and technological progress, innovation and development and high-level talent training from tens of thousands of literatures marked with important national science and technology projects and a large number of grey system literatures published by China’s double first-class universities and double first-class discipline construction universities.

Both innovations of theoretical research and practical application play important role in the growth of new theory. The innovations of theoretical research provide methods and tools for practical application, which is conducive to improve application efficiency and broaden application fields. A large number of practical applications needs have become the source of theoretical innovation and the solid background for the birth of theoretical innovation achievements.

The purpose of this paper is to address and overcome the problem that a single prediction model cannot accurately fit a data sequence with large fluctuations.

Initially, the grey linear regression combination model was put forward. The Discrete Grey Model (DGM)(1,1) model and the multiple linear regression model were then combined using the entropy weight method. The grain yield from 2010 to 2015 was forecasted using DGM(1,1), a multiple linear regression model, the combined model and a GM(1,N) model. The predicted values were then compared against the actual values.

The results reveal that the combination model used in this paper offers greater simulation precision. The combination model can be applied to the series with fluctuations and the weights of influencing factors in the model can be objectively evaluated. The simulation accuracy of GM(1,N) model fluctuates greatly in this prediction.

The combined model adopted in this paper can be applied to grain forecasting to improve the accuracy of grain prediction. This is important as data on grain yield are typically characterised by large fluctuation and some information is often missed.

This paper puts the grey linear regression combination model which combines the DGM(1,1) model and the multiple linear regression model using the entropy weight method to determine the results weighting of the two models. It is intended that prediction accuracy can be improved through the combination of models used within this paper.

The aim of this paper is to present the first diffusion analysis of ISO/IEC 27001, the fourth most popular ISO certification at global level and the most important standard for information security.

To achieve the purposes, the authors applied Grey Models (GM) – Even GM (1,1), Even GM (1,1,α,θ), Discrete GM (1,1), Discrete GM (1,1,α) – complemented by the relative growth rate and the doubling time indexes on the six most important countries in terms of issued certificates.

Results show that a growing trend is likely to be expected in the years to come and that China will lead at country level.

The study contributes to the scientific debate by presenting the first diffusive analysis of ISO/IEC 27001 and by proposing a forecasting approach that to date has found little application in the field of international standards.

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.

In order to more accurately predict the dynamics of the e-commerce market and increase the comprehensive value of the circular e-commerce industry, proposes to use Grey system theory to analyze the circular economy of the e-commerce market.

Construct a Grey system theory model, analyze the big data of e-commerce and circular economy of the e-commerce market and predict the development potential of China's e-commerce market.

The results show that the Grey system theory model can play an important role in the data analysis of circular economy of the e-commerce market.

Use Grey model to analyze e-commerce data, discover e-commerce market rules and problems and then optimize e-commerce market.

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.