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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.

To develop the theory and application of the grey prediction model, this investigation constructs a novel discrete grey Riccati model termed DGRM(1,1).

By examining a special kind of Riccati difference equation and the structure of the conventional discrete grey model (DGM), we advance a novel DGRM, and the model's prediction effect is evaluated by two numerical examples and an application case and compared with that of other conventional grey models.

The average relative simulation error of DGRM(1,1) does not change if the model is built after the original sequence has been transformed by a multiplier, and the new model is suitable to predict monotonically increasing, monotonically decreasing and unimodal sequences.

DGRM(1,1) is utilized to forecast the development cost of a small plane owned by the Aviation Industry Corporation of China (AVIC) with an original data sequence from 2006 to 2013. The outcomes indicate that DGRM(1,1) exhibits high precision and potential in development cost prediction.

Combining the Riccati difference equation with the conventional DGM, the author advances a new grey model that is suitable to predict three kinds of data series with different changing trends.

The global warming, caused by the anthropogenic greenhouse gases, has been one of the major worldwide issues over the last decades. Among them, carbon dioxide (CO₂) is the most important one and is responsible for more than the two-third of the greenhouse effect. Currently, greenhouse gas emissions and CO₂ emissions – the root cause of the global warming – in particular are being examined closely in the fields of science and they also have been put on the agenda of the political leaders. The purpose of this paper is to predict the energy-related CO₂ emissions through using different discrete grey models (DGMs) in Turkey and total Europe and Eurasia region.

The proposed DGMs will be applied to predict CO₂ emissions in Turkey and total Europe and Eurasia region from 2015 to 2030 using data set between 1965 and 2014. In the first stage of the study, DGMs without rolling mechanism (RM) will be used. In the second stage, DGMs with RM are constructed where the length of the rolling horizons of the respected models is optimised.

In the first stage, estimated values show that non-homogeneous DGM is the best method to predict Turkey’s energy-related CO₂ emissions whereas DGM is the best method to predict the energy-related CO₂ emissions for total Europe and Eurasia region. According to the results in the second stage, NDGM with RM (k=26) is the best method for Turkey while optimised DGM with RM (k=4) delivers most reliable estimates for total Europe and Eurasia region.

This study illustrates the effect of different DGM approaches on the estimation performance for the Turkish energy-related CO₂ emission data.

Due to high efficiency and low carbon of natural gas, the consumption of natural gas is increasing rapidly, and the prediction of natural gas consumption has become the focus. The purpose of this paper is to employ a prediction technique by combining grey prediction model and trigonometric residual modification for predicting average per capita natural gas consumption of households in China.

The GM(1,1) model is utilised to obtain the tendency term, then the generalised trigonometric model is used to catch the periodic phenomenon from the residual data of GM(1,1) model for improving predicting accuracy.

The case verified the view of Xie and Liu: “When the value of a is less, DGM model and GM(1,1) model can substitute each other.” The combination of the GM(1,1) and the trigonometric residual modification technique can observably improve the predicting accuracy of average per capita natural gas consumption of households in China. The mean absolute percentage errors of GM(1,1) model, DGM(1,1), unbiased grey forecasting model, and TGM model in ex post testing stage (from 2013 to 2015) are 32.5510, 33.5985, 36.9980, and 5.2996 per cent, respectively. The TGM model is suitable for the prediction of average per capita natural gas consumption of households in China.

According to the historical data of average per capita natural gas consumption of households in China, the authors construct GM(1,1) model, DGM(1,1) model, unbiased grey forecasting model, and GM(1,1) model with trigonometric residual modification. The accuracy of TGM is the best. TGM helps to improve the accuracy of GM(1,1).

This paper gives a successful practical application of grey model GM(1,1) with the trigonometric residual modification, where the cyclic variations exist in the residual series. The case demonstrates the effectiveness of trigonometric grey prediction model, which is helpful to understand the modeling mechanism of trigonometric grey prediction model.

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 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 clarify several commonly used quality cost models based on Juran’s characteristic curve. Through mathematical deduction, the lowest point of quality cost and the lowest level of quality level (often depicted by qualification rate) can be obtained. This paper also aims to introduce a new prediction model, namely discrete grey model (DGM), to forecast the changing trend of quality cost.

This paper comes to the conclusion by means of mathematical deduction. To make it more clear, the authors get the lowest quality level and the lowest quality cost by taking the derivative of the equation of quality cost and quality level. By introducing the weakening buffer operator, the authors can significantly improve the prediction accuracy of DGM.

This paper demonstrates that DGM can be used to forecast quality cost based on Juran’s cost characteristic curve, especially when the authors do not have much information or the sample capacity is rather small. When operated by practical weakening buffer operator, the randomness of time series can be obviously weakened and the prediction accuracy can be significantly improved.

This paper uses a real case from a literature to verify the validity of discrete grey forecasting model, getting the conclusion that there is a certain degree of feasibility and rationality of DGM to forecast the variation tendency of quality cost.

This paper perfects the theory of quality cost based on Juran’s characteristic curve and expands the scope of application of grey system theory.

The purpose of this paper is to expand discrete GM (1,1) model and solve the problem of non‐equidistance grey prediction problem with integral interval or digital interval.

Discrete GM (1,1) model can be utilized to simulate exponential sequence without errors, but it can't be utilized to simulate non‐equidistance data sequence. This paper applied optimization theories to establish generalized discrete GM (1,1) model. First, this paper established the time response of simulation sequence directly. Second, this paper established the steps of non‐equidistance data sequence. Finally, this paper utilized examples to test the method put forward.

The results indicate the generalized discrete GM (1,1) (GDGM) model can perfectly simulate non‐equidistance exponential series. Discrete GM (1,1) model is only the special form of GDGM model.

Though grey forecasting models are widely used, most of the forecasting models are based on the equal distance sequence. Due to many reasons, the raw data available usually is incomplete. There are mainly four reasons which caused non‐equidistance sequence. So generalized discrete GM (1,1) model can be utilized to simulate non‐equidistance sequence and has great application values.

The paper succeeds in establishing a generalized discrete GM (1,1) model which can be utilized to solve non‐equidistance data sequence forecasting. The GDGM model can be solved by MATLAB or other corresponding software.

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.

In order to accurately forecast nonlinear and complex characteristics of solar power generation in China, a novel discrete grey model with time-delayed power term (abbreviated as TDDGM(1,1,tα) is proposed in this paper.

Firstly, the time response function is deduced by using mathematical induction, which overcomes the defects of the traditional grey model. Then, the genetic algorithm is employed to determine the optimal nonlinear parameter to improve the flexibility and adaptability of the model. Finally, two real cases of installed solar capacity forecasting are given to verify the proposed model, showing its remarkable superiority over seven existing grey models.

Given the reliability and superiority of the model, the model TDDGM(1,1,tα) is applied to forecast the development trend of China's solar power generation in the coming years. The results show that the proposed model has higher prediction accuracy than the comparison models.

This paper provides a scientific and efficient method for forecasting solar power generation in China with nonlinear and complex characteristics. The forecast results can provide data support for government departments to formulate solar industry development policies.

The main contribution of this paper is to propose a novel discrete grey model with time-delayed power term, which can handle nonlinear and complex time series more effectively. In addition, the genetic algorithm is employed to search for optimal parameters, which improves the prediction accuracy of the model.