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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 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 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.

Sparrow search algorithm (SSA) is a novel global optimization method, but it is easy to fall into local optimization, which leads to its poor search accuracy and stability. The purpose of this study is to propose an improved SSA algorithm, called levy flight and opposition-based learning (LOSSA), based on LOSSA strategy. The LOSSA shows better search accuracy, faster convergence speed and stronger stability.

To further enhance the optimization performance of the algorithm, The Levy flight operation is introduced into the producers search process of the original SSA to enhance the ability of the algorithm to jump out of the local optimum. The opposition-based learning strategy generates better solutions for SSA, which is beneficial to accelerate the convergence speed of the algorithm. On the one hand, the performance of the LOSSA is evaluated by a set of numerical experiments based on classical benchmark functions. On the other hand, the hyper-parameter optimization problem of the Support Vector Machine (SVM) is also used to test the ability of LOSSA to solve practical problems.

First of all, the effectiveness of the two improved methods is verified by Wilcoxon signed rank test. Second, the statistical results of the numerical experiment show the significant improvement of the LOSSA compared with the original algorithm and other natural heuristic algorithms. Finally, the feasibility and effectiveness of the LOSSA in solving the hyper-parameter optimization problem of machine learning algorithms are demonstrated.

An improved SSA based on LOSSA is proposed in this paper. The experimental results show that the overall performance of the LOSSA is satisfactory. Compared with the SSA and other natural heuristic algorithms, the LOSSA shows better search accuracy, faster convergence speed and stronger stability. Moreover, the LOSSA also showed great optimization performance in the hyper-parameter optimization of the SVM model.

The purpose of this paper is to summarize the progress in grey system research during 2000-2015, so as to present some important new concepts, models, methods and a new framework of grey system theory.

The new thinking, new models and new methods of grey system theory and their applications are presented in this paper. It includes algorithm rules of grey numbers based on the “kernel” and the degree of greyness of grey numbers, the concept of general grey numbers, the synthesis axiom of degree of greyness of grey numbers and their operations; the general form of buffer operators of grey sequence operators; the four basic models of grey model GM(1,1), such as even GM, original difference GM, even difference GM, discrete GM and the suitable sequence type of each basic model, and suitable range of most used grey forecasting models; the similarity degree of grey incidences, the closeness degree of grey incidences and the three-dimensional absolute degree of grey incidence of grey incidence analysis models; the grey cluster model based on center-point and end-point mixed triangular whitenization functions; the multi-attribute intelligent grey target decision model, the two stages decision model with grey synthetic measure of grey decision models; grey game models, grey input-output models of grey combined models; and the problems of robust stability for grey stochastic time-delay systems of neutral type, distributed-delay type and neutral distributed-delay type of grey control, etc. And the new framework of grey system theory is given as well.

The problems which remain for further studying are discussed at the end of each section. The reader could know the general picture of research and developing trend of grey system theory from this paper.

A lot of successful practical applications of the new models to solve various problems have been found in many different areas of natural science, social science and engineering, including spaceflight, civil aviation, information, metallurgy, machinery, petroleum, chemical industry, electrical power, electronics, light industries, energy resources, transportation, medicine, health, agriculture, forestry, geography, hydrology, seismology, meteorology, environment protection, architecture, behavioral science, management science, law, education, military science, etc. These practical applications have brought forward definite and noticeable social and economic benefits. It demonstrates a wide range of applicability of grey system theory, especially in the situation where the available information is incomplete and the collected data are inaccurate.

The reader is given a general picture of grey systems theory as a new model system and a new framework for studying problems where partial information is known; especially for uncertain systems with few data points and poor information. The problems remaining for further studying are identified at the end of each section.

As an important measure to promote sustainable development, green finance has developed rapidly in recent years. In order to comprehensively analyze the positive and negative indicators of the influencing factors of green finance, this paper puts forward a grey relational method of spatial-temporal panel data from the perspective of the development trend of the object dimension indicators and the performance difference between the time dimension indicators.

From the different perspectives of object dimension and time dimension, the positive and negative indicators are standardized differently considering the reverse of indicators and characterizing factors. The grey absolute relational degree is used to define the matrix sequence. This method reflects the development trend of objects in time and the difference characteristics among objects, which comprehensively represents the correlation between the reference panel and the comparison panel.

The results show that: (1) The object dimension reflects the internal driving force of the development of green finance in each provincial administrative region and the time dimension reflects the relationship between regional differences of influencing factors and green finance. (2) From the object dimension, the influencing factors of green finance from high to low are economic development potential, economic development level, air temperature, policy support, green innovation and air quality. (3) From the time dimension, the influencing factors of green finance from high to low are green innovation, air quality, economic development potential, economic development level, policy support and air temperature.

The different standardized processing methods of positive and negative indicators proposed in this paper not only eliminate the sample dimension, but also study the grey relational degree among the indicator panels from different reference dimensions. The proposed model is applied to identify the influencing factors of green finance, which expands the practical application scope of the grey relational model. The research results can provide reference for relevant departments to better promote the development of green finance.

The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.

Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.

The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space.

The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.

The purpose of this paper is to establish the grey relational estimating model of soil pH value based on hyper-spectral data.

As to the uncertainty of the factors affecting the soil pH value estimation based on hyper-spectral, the grey weighted relation estimation model was set up according to the grey system theory. Then the linear regression correction model is established according to the difference and grey relation degree information between the estimated samples and their corresponding pattern. At the same time, the model was applied to Hengshan county of Shanxi province.

The results are convincing: not only that the linear regression correction model of grey relation estimating pattern of soil pH value based on hyper-spectral data is valid, but also the model’s estimating accuracy is higher, which the corrected average relative error is 0.2578 per cent, and the decision coefficient R²=0.9876.

The method proposed in the paper can be used at soil pH value hyper-spectral inversion and even for other similar forecast problem.

The paper succeeds in realising both the soil pH value hyper-spectral grey relation estimating pattern based on the grey relational theory and the correction model of the estimating pattern by using the linear regression.