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Prediction problems raised in uncertain environments require different solution approaches such as grey prediction models, which consider uncertainty in information and also enable the use of small data sets. The purpose of this paper is to investigate the comparative performances of grey prediction models (GM) and Markov chain integrated grey models in a demand prediction problem.

The modeling process of grey models is initially described, and then an integrated model called the Grey-Markov model is presented for the convenience of applications. The analyses are conducted on a monthly demand prediction problem to demonstrate the modeling accuracies of the GM (1,1), GM (2,1), GM (1,1)-Markov, and GM (2,1)-Markov models.

Numerical results reveal that the Grey-Markov model based on GM (2,1) achieves better prediction performance than the other models.

It is thought that the methodology and the findings of the study will be a significant reference for both academics and executives who struggle with similar demand prediction problems in their fields of interest.

The novelty of this study comes from the fact that the GM (2,1)-Markov model has been first used for demand prediction. Furthermore, the GM (2,1)-Markov model represents a relatively new approach, and this is the second paper that addresses the GM (2,1)-Markov model in any area.

The purpose of this paper is to employ the Grey-Markov Chain Model for the scale prediction of cultivated land and took an empirical research with the case of Jiangsu province.

Along with China’s industrialization and urbanization accelerated, a large number of cultivated land converse into construction land. The change of utilization of cultivated land concerns national food security and sustainable development of economy and society. Due to the fact that the different investigation methods of arable land usually cause a uncertain. The Grey-Markov model combines the Grey GM(1,1) and Markov chain, with two advantages of dealing with poor information and long-term and volatile series. A numeric example of scale prediction of cultivated land in Jiangsu province is also computed in the third part of the paper.

The results show that the Grey-Markov Chain Model has a higher prediction accuracy compared with GM (1,1), which is a reliable guarantee for the change of cultivated land resources.

The forecast of cultivated land can provide useful information for the general land use planning.

The paper confirmed the feasibility of the Grey-Markov model in scale prediction of cultivated land.

Many factors affect the emergence and development of crop diseases and insect pests. Traditional methods for investigating this subject are often difficult to employ and produce limited data with considerable uncertainty. The purpose of this paper is to predict the annual degree of cotton spider mite infestations by employing grey theory.

The authors established a GM(1,1) model to forecast mite infestation degree based on the analysis of historical data. To improve the prediction accuracy, the authors modified the grey model using Markov chain and BP neural network analyses. The prediction accuracy of the GM(1,1), Grey-Markov chain, and Grey-BP neural network models was 84.31, 94.76, and 96.84 per cent, respectively.

Compared with the single grey forecast model, both the Grey-Markov chain model and the Grey-BP neural network model had higher forecast accuracy, and the accuracy of the latter was highest. The improved grey model can be used to predict the degree of cotton spider mite infestations with high accuracy and overcomes the shortcomings of traditional forecasting methods.

The two new models were used to estimate mite infestation degree in 2015 and 2016. The Grey-Markov chain model yielded respective values of 1.27 and 1.15, whereas the Grey-BP neural network model yielded values 1.4 and 1.68; the actual values were 1.5 and 1.8.

The improved grey model can be used for medium- and long-term predictions of the occurrence of cotton spider mites and overcomes problems caused by data singularity and fluctuation. This research method can provide a reference for the prediction of similar diseases.

The purpose of this paper is to analyse the results of energy audit reports and defines most favourable characteristics of system, which is energy consumption of buildings, and most favourable factors affecting these characteristics in order to modify and improve them.

Grey set theory has the advantage of using fewer data to analyse many factors, and it is therefore more appropriate for system study rather than traditional statistical regression which requires massive data, normal distribution in the data and few variant factors. So, in this paper grey clustering and entropy of coefficient vector of grey evaluations are used to analyse energy consumption in buildings of the Oil Ministry in Tehran. Grey clustering in this study has been used for two purposes: First, all the variables of building relate to energy audit cluster in two main groups of indicators and the number of variables is reduced. Second, grey clustering with variable weights has been used to classify all buildings in three categories named “no standard deviation”, “low standard deviation” and “non-standard”. Entropy of coefficient vector of grey evaluations is calculated to investigate greyness of results.

According to the results of the model, “the real building load coefficient” has been selected as the most important system characteristic and “uncontrolled area of the building” has been diagnosed as the most favourable factor which has the greatest effect on energy consumption of building.

Clustering greyness of 13 buildings is less than 0.5 and average uncertainly of clustering results is 66 per cent.

It shows that among the 38 buildings surveyed in terms of energy consumption, three cases are in standard group, 24 cases are in “low standard deviation” group and 11 buildings are completely non-standard.

In this research, a comprehensive analysis of the audit reports is proposed. This analysis helps the improvement of future audits, and assists in making energy conservation policies by studying the behaviour of system characteristic and related factors.

Since the issuance in 2009, the digital currency has enjoyed an increasing popularity and has become one of the most important options for global investors. The purpose of this paper is to propose a hybrid model ( KDJ–Markov chain) which integrates the advantages of the stochastic index (KDJ) and grey Markov chain methods and provide a useful decision support tool for investors participating in the digital currency market.

Taking Litecoin's closing price prediction as an example, the closing prices from May 2 to June 20, 2017, are used as the training set, while those from June 21 to August 9, 2017, are used as the test set. In addition, an adaptive KDJ–Markov chain is proposed to enhance the adaptability for dynamic transaction information. And the paper verifies the effectiveness of the KDJ–Markov chain method and adaptive KDJ–Markov chain method.

The results show that the proposed methods can provide a reliable foundation for market analysis and investment decisions. Under the circumstances the accuracy of the training set and the accuracy of the test set are 76% and 78%, respectively.

This study not only solves the problems that KDJ method cannot accurately predict the next day's state and the grey Markov chain method cannot divide the states very well, but it also provides two useful decision support tools for investors to make more scientific and reasonable decisions for digital currency where there are no existing methods to analyze the fluctuation.

A new approach to analyze the fluctuation of digital currency, in which there are no existing methods, is proposed based on the stochastic index (KDJ) and grey Markov chain methods. And both of these two models have high accuracy.

The purpose of this paper is to investigate the effect of round pits arrangement patterns on tribological properties of journal bearing. In this paper, the tribological behaviors of journal bearing with different arrangement patterns under lubrication condition were studied based on M-2000 friction and wear tester.

The friction and wear of journal bearing contact surface were simulated by ANSYS. The wear mechanism of bearing contact surfaces was investigated by the means of energy dispersive spectrum analysis on the surface morphology and friction and wear status of the journal bearing specimens by Scanning Electron Microscopy (SEM) and Energy Dispersive Spectrometer (EDS). Besides, the wearing capacity of the textured bearing was predicted by using the GM (1,1) and Grey–Markov model.

As the loads increase, the friction coefficient of journal bearing specimens decrease first and then increase slowly. The higher rotation speed, the lower friction coefficient and the faster temperature build-up. The main friction method of the bearing sample is three-body friction. The existence of texture can effectively reduce friction and wear. In many arrangement patterns, the best is 4# bearing with round pits cross-arrangement pattern. Its texturing diameters are 60 µm and 125 µm, and the spacing and depth are 200 µm and 25 µm, respectively. In addition, the Grey–Markov model prediction result is more accurate and fit the experimental value better.

The friction and wear mechanism is helpful for scientific research and engineers to understand the tribological behaviors and engineering applications of textured bearing. The wear capacity of textured bearing is predicted by using the Grey–Markov model, which provides technical help and theoretical guidance for the service life and reliability of textured bearing.

The purpose of this paper is to present a method to accurately forecast the tendency of the gross amount of energy sources consumption of the country and construct a new kind of algorithm for forecasting that synthesizes the advantages of the grey model, Markov chains, and least square method.

With the application of this new algorithm, this paper have forecasted the trend of the gross amount of energy sources consumption of the country and come to the conclusions that the new algorithm is more precise than the grey model. It is proved that the improved grey‐Markov chain algorithm is effective and can be used by authorities to make decision.

It was found that combining the grey model, Markov chains, and least square method, can be a new algorithm for forecasting the trendency of the gross amount of energy sources consumption.

The new algorithm is only suitable for the short‐term forecast.

The grey forecasting method reflects the overall tendency of primitive data sequence of the gross amount of energy source, and the Markov chain forecasting method reflects the effect of the random fluctuation. The least square method reflects the tendency of increase. The new algorithm is more precise than the grey model.

The purpose of this paper is to improve the forecasting efficiency of a grey model.

The exponentially weighted moving average (EWMA) algorithm is proposed to modify background values for a new grey model optimization.

The experimental results reveal that the proposed models (EGM, REGM) outperform traditional grey models.

A genetic algorithm (GA) optimizer is used to select the optimal weights for the background values of the EGM(1,1) and REGM(1,1) forecast models. The results of the current study are very encouraging, as the empirical results show that the REGM(1,1) and EGM(1,1) models reduce the MAPE rates over the traditional GM(1,1) and RGM(1,1) models.

The purpose of this paper is to summarize the different types of grey information, explain the mechanism of grey system modeling and reconstruct the framework of grey system theory (GST).

GST has been developed for more than three decades; however, the framework of GST is still in an evolutionary process. This manuscript first explains grey information in detail, and then summarizes a series of grey system models under limited data and poor information. Figures and general steps for different types of grey system models are provided in this paper.

The findings in this paper clearly differentiate between grey information and other uncertainty information. The differences between grey system models and other uncertainty models are clearly explained. In addition, general steps for different grey system models are given which demonstrate the orientation of grey system modeling.

Theoretical framework is very important for developing a new theory. This paper clarified grey information and grey system-based modeling mechanism. It is very useful to understand and explain the systematic framework of GST and it contributes undoubtedly to make GST perfect.

Grey information is explained in terms of limited data and two types of grey numbers. Accordingly, all of the grey system models were divided into limited data-based grey system models and grey number-based grey system models.

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.