Grey system model with the fractional order accumulation

Wu, Lifeng; Liu, Sifeng; Yao, Ligen; Yan, Shuli; Liu, Dinglin

doi:10.1016/j.cnsns.2012.11.017

Cited by 513 publications

(265 citation statements)

References 24 publications

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“…It has been studied by many researchers and improved over the years [20][21][22]. Recently, Liu et al [23], Wu et al [24,25], and Xiao et al [26,27] published results on fractional order accumulation and grey system model with the fractional order accumulation. However, all the existing research [28,29] does not deduce the analytical expression of fractional order accumulating generation operator and fractional order reducing generation operator, nor does it prove that these fractional order generation operators satisfy mutual invertibility.…”

Section: Introductionmentioning

confidence: 99%

Prediction of China’s Sulfur Dioxide Emissions by Discrete Grey Model with Fractional Order Generation Operators

2018

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Sulfur dioxide is an important source of atmospheric pollution. Many countries are developing policies to reduce sulfur dioxide emissions. In this paper, a novel prediction model is proposed, which could be used to forecast sulfur dioxide emissions. To improve the modeling procedure, fractional order accumulating generation operator and fractional order reducing generation operator are introduced. Based on fractional order operators, a discrete grey model with fractional operators is developed, which also makes use of genetic algorithms to optimize the modeling parameter . The improved performance of the model is demonstrated via comparison studies with other grey models. The model is then used to predict China's sulfur dioxide emissions. The forecast result shows that the amount of sulfur dioxide emissions is steadily decreasing and the policies of sulfur dioxide reduction in China are effective. According to the current trend, by 2020, the value of China's sulfur dioxide emissions will be only 86.843% of emissions in 2015. Fractional order generation operators can be used to develop other fractional order system models.

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Section: Introductionmentioning

confidence: 99%

Prediction of China’s Sulfur Dioxide Emissions by Discrete Grey Model with Fractional Order Generation Operators

2018

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“…Grey system theory is developed by Deng [7]. As the primary forecasting method of grey system theory, GM(1,1) has been applied in many fields [4][5][6][7]. However, GM(1,1) is suitable for the stable time series, how to predict the nonstationary series is a difficult problem which deserves to research.…”

Section: Introductionmentioning

confidence: 99%

“…Over the years, many scholars have carried out vigorous programs [1][2][3][4]. Among these programs, it is reported that the forecasting performance of grey model is better than many conventional methods with incomplete or insufficient data [4][5][6]. Grey system theory is developed by Deng [7].…”

Section: Introductionmentioning

confidence: 99%

Using the fractional order method to generalize strengthening buffer operator and weakening buffer operator

Liu

Yang

2018

IEEE/CAA J. Autom. Sinica

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Abstract-Traditional integer order buffer operator is extended to fractional order buffer operator, the corresponding relationship between the weakening buffer operator and the strengthening buffer operator is revealed. Fractional order buffer operator not only can generalize the weakening buffer operator and the strengthening buffer operator, but also realize tiny adjustment of buffer effect. The effectiveness of GM(1,1) with the fractional order buffer operator is validated by six cases.Index Terms-fractional order; grey system theory; strengthening buffer operator; weakening buffer operator.

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“…However, the accumulation of integer order was not suitable for some data, as modeling, and the effects of simulation and prediction were poor. Nevertheless, the current fraction grey model which used factional order accumulation [24][25][26][27] has the important significance for improving the performance of grey model. Therefore, Wu et al [28] defined the actual data with fractional order accumulation and defined the NDGM model with fractional order accumulation (NDGM 푝/푞 ).…”

Section: Introductionmentioning

confidence: 99%

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

Duan

Shao

Xiao

et al. 2017

Mathematical Problems in Engineering

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The grey forecasting model has been successfully applied in numerous fields since it was proposed. The nonhomogeneous discrete grey model (NDGM) was approximately constructed based on the nonhomogeneous index trend; it increased the applicability of discrete grey model. However, the NDGM required accurate data and better effect when the original data did not meet the conditions and fitting and prediction errors were larger. For this, the NDGM with the fractional order accumulating operator (abbreviated as NDGM 푝/푞 ) has higher performance. In this paper, the matrix perturbation bound of the parameters was used to analyze the stability of NDGM 푝/푞 and the NDGM 푝/푞 can decrease the disturbance bound. Subsequently, the parameter estimation method of NDGM 푝/푞 was studied and the Particle Swarm Optimization algorithm was employed to optimize the order number of NDGM 푝/푞 and some steps were provided. In addition, the results of two practical examples demonstrated that the perturbation of NDGM 푝/푞 was smaller than that of NDGM and provided remarkable predication performance compared with the traditional NDGM model and DGM model.

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Grey system model with the fractional order accumulation

Cited by 513 publications

References 24 publications

Prediction of China’s Sulfur Dioxide Emissions by Discrete Grey Model with Fractional Order Generation Operators

Prediction of China’s Sulfur Dioxide Emissions by Discrete Grey Model with Fractional Order Generation Operators

Using the fractional order method to generalize strengthening buffer operator and weakening buffer operator

Research on the Stability of NDGM Model with the Fractional Order Accumulation and Its Optimization

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