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The ability to forecast a trend is very important in energy consumption prediction and energy production planning. The principle, under which the grey systems theory is applied in our energy consumption prediction, is that the forecasting system can be considered as a grey system. In such a system, unknown system's information can be determined by using known information. Here, the known information consists of energy consumption data, development trend in the consumption system. Based on our study, we eventually make forecast and decisions regarding possible future development. Our method is a whitenization process of a grey course. The model developed is based on the division method established for general data modelling and estimation of parameters of GM(1,1) its standard error coefficient that was applied to judge the accuracy height of the model was put forward; further, the function transform to forecast energy consuming trend and assess GM(1, 1) parameter was established. These two models need not pre‐process the primitive data. It was not only suited for equal interval data modeling, but also for non‐equal interval data modeling. Its calculation was simple and used conveniently, and the oil consumption per unit output analysis was taken as an example. The example showed that the two models were simple and practical, it was worth expanding and applying in the energy consuming prediction and energy programming.

The purpose of this paper is to predict hospital respiratory system infection rate by using the gray GM(1,1) model, and to provide theoretical basis for the prospective study on hospital respiratory system infection management.

The annual respiratory system infection rate of a comprehensive third-class hospital in Yan’an is collected from 2011 to 2017. The GM(1,1) model is used for prediction, and mean absolute percentage error is used to evaluate the prediction accuracy of the model.

GM(1,1) statistical prediction model is established with good fitting degree and high reliability of extrapolation prediction.

The GM(1,1) model can well predict the respiratory system infection rate of the hospital.

The purpose of this paper is to overcome the deficiency of the current GM(1,N) such as low‐prediction precision, extend the scope of GM(1,N) and provide an effective grey dynamic model GM(1,N) for the relationship of cost and variability.

The relationship between two factors of variety and the cost of manufacturing system is studied on the basis of the variety reduction program theory. Based on the Grey system and the gradient algorithm, a Grey dynamic model GM(1,N) is proposed between cost and variety by optimizing the coefficient and background value of the model which is used to check validity for the relation of plasm‐yarn machine product and variety.

The proposed Grey dynamic prediction model GM(1,N) for the relationship of cost and variability has high precision and easy‐to‐use.

A Grey model GM(1,N) for prediction is proposed.

The proposed model should also have potential for multifactor system prediction in engineering.

The deficiency of the current GM(1,N) is overcome, the scope of GM(1,N) is extended and the proposed Grey dynamic model GM(1,N) has high‐prediction precision.

This study aims to predict China's carbon emission intensity and put forward a set of policy recommendations for further development of a low-carbon economy in China.

In this paper, the Interaction Effect Grey Power Model of N Variables (IEGPM(1,N)) is developed, and the Dragonfly algorithm (DA) is used to select the best power index for the model. Specific model construction methods and rigorous mathematical proofs are given. In order to verify the applicability and validity, this paper compares the model with the traditional grey model and simulates the carbon emission intensity of China from 2014 to 2021. In addition, the new model is used to predict the carbon emission intensity of China from 2022 to 2025, which can provide a reference for the 14th Five-Year Plan to develop a scientific emission reduction path.

The results show that if the Chinese government does not take effective policy measures in the future, carbon emission intensity will not achieve the set goals. The IEGPM(1,N) model also provides reliable results and works well in simulation and prediction.

The paper considers the nonlinear and interactive effect of input variables in the system's behavior and proposes an improved grey multivariable model, which fills the gap in previous studies.

The purpose of this paper is to deal with the ill‐conditioned problem for the non‐equigap GM(1,1) control model by using the method of multiple transformations.

Owing to noises and interferences from both inside and outside of the system, many control systems contain unequal intervals and sharp variation which may result in undesirable systems instability. In order to ensure the stability and efficiency of grey forecasting control model, the data transformation for a raw series is an important and useful method for enhancing accuracy and improving ill‐condition of the non‐equigap GM(1,1) model.

This paper discusses the quantitative relations between the multiple transformation and the parameters of the non‐equigap GM(1,1) model in detail, and studies the effect of the multiple transformation on the condition number of the non‐equigap GM(1,1) model.

Accessibility and availability of data are the main limitations based on which model will be applied.

Choosing an appropriate multiple of transformation cannot only eliminate dimension, lessen computation and maintain high accuracy, but also largely reduce the condition number of the model and improve the ill‐condition of non‐equigap GM(1,1) model effectively.

This paper seems to be the first to discuss the stability problems for the non‐equigap GM(1,1) model.

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.

In this study, a new neural differential grey model is proposed for the purpose of accurately excavating the evolution of real systems.

For this, the proposed model introduces a new image equation that is solved by the Runge-Kutta fourth order method, which makes it possible to optimize the sequence prediction function. The novel model can then capture the characteristics of the input data and completely excavate the system's evolution law through a learning procedure.

The new model has a broader applicability range as a result of this technique, as opposed to grey models, which have fixed structures and are sometimes over specified by too strong assumptions. For experimental purposes, the neural differential grey model is implemented on two real samples, namely: production of crude and consumption of Cameroonian petroleum products. For validation of the new model, results are compared with those obtained by competing models. It appears that the precisions of the new neural differential grey model for prediction of petroleum products consumption and production of Cameroonian crude are respectively 16 and 25% higher than competing models, both for simulation and validation samples.

This article also takes an in-depth look at the mechanics of the new model, thereby shedding light on the intrinsic differences between the new model and grey competing models.

When performing system-level developmental testing, time and expenses generally warrant a small sample size for failure data. Upon failure discovery, redesigns and/or corrective actions can be implemented to improve system reliability. Current methods for estimating discrete (one-shot) reliability growth, namely the Crow (AMSAA) growth model, stipulate that parameter estimates have a great level of uncertainty when dealing with small sample sizes. The purpose of this paper is to present an application of a modified GM(1,1) model for handling system-level testing constrained by small sample sizes.

The paper presents a methodology for incorporating failure data into a modified GM(1,1) model for systems with failures following a poly-Weibull distribution. Notional failure data are generated for complex systems and characterization of reliability growth parameters is performed via both the traditional AMSAA model and the GM(1,1) model for purposes of comparing and assessing performance.

The modified GM(1,1) model requires less complex computational effort and provides a more accurate prediction of reliability growth model parameters for small sample sizes and multiple failure modes when compared to the AMSAA model. It is especially superior to the AMSAA model in later stages of testing.

This research identifies cost-effective methods for developing more accurate reliability growth parameter estimates than those currently used.

In recent years, domestic smog has become increasingly frequent and the adverse effects of smog have increasingly become the focus of public attention. It is a way to analyze such problems and provide solutions by mathematical methods.

This paper establishes a new gray model (GM) (1,N) prediction model based on the new kernel and degree of grayness sequences under the case that the interval gray number distribution information is known. First, the new kernel and degree of grayness sequences of the interval gray number sequence are calculated using the reconstruction definition of the kernel and degree of grayness. Then, the GM(1,N) model is formed based on the above new sequences to simulate and predict the kernel and degree of the grayness of the interval gray number sequence. Finally, the upper and lower bounds of the interval gray number are deduced based on the calculation formulas of the kernel and degree of grayness.

To verify further the practical significance of the model proposed in this paper, the authors apply the model to the simulation and prediction of smog. Compared with the traditional GM(1,N) model, the new GM(1,N) prediction model established in this paper has better prediction effect and accuracy.

This paper improves the traditional GM(1,N) prediction model and establishes a new GM(1,N) prediction model in the case of the known distribution information of the interval gray number of the smog pollutants concentrations data.

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.