Soft Computing

, Volume 23, Issue 23, pp 12873–12881 | Cite as

Discrete grey model with the weighted accumulation

  • Lifeng WuEmail author
  • Hongying Zhao
Methodologies and Application


To add greater weight to new information, discrete grey model with the weighted accumulation (WDGM(1,1)) is put forward. This paper proved the stability of WDGM(1,1) disturbance boundary and the influence of the analysis parameter λ on the reduction error. The prediction ability of the WDGM(1,1) is verified by five cases. The results show that WDGM(1,1) not only satisfies the new information priority to a certain extent, but also has better stability. Moreover, the parameter λ in WDGM(1,1) can effectively reduce the reduction error, so that it has better prediction accuracy in practical applications. Therefore, the proposal of WDGM(1,1) is not only very theoretical, but also has good practical significance.


Grey model Weighted accumulation Disturbance boundary Reduction error 



The relevant researches carried out in this paper are supported by the National Natural Science Foundation of China (Nos. 71871084, 71401051).

Compliance with ethical standards

Conflict of interest

The authors declare that they have no conflict of interest.

Ethical approval

This article does not contain any studies with human participants or animals.


  1. Chen CI, Hsin PH, Wu CS (2010) Forecasting Taiwan’s major stock indices by the Nash nonlinear grey Bernoulli model. Expert Syst Appl 37(12):7557–7562CrossRefGoogle Scholar
  2. Dang YG, Liu SF, Liu B (2005) The GM models that x(1)(n) be taken as initial value. Chin J Manag Sci 13(1):133–136Google Scholar
  3. Ding S, Dang YG, Li XM, Wang JJ, Zhao K (2017) Forecasting Chinese CO2 emissions from fuel combustion using a novel grey multivariable model. J Clean Prod 162:1527–1538CrossRefGoogle Scholar
  4. Han Z (1995) Application of exponential cumulative generation method and logarithmic cumulative generation method to grey prediction. China J Highw Transp 8(1):52–57Google Scholar
  5. Hu P (2016) The DGM(1,1) models that x(1)(n) be taken as initial value. Math Pract Theory 46(17):218–222MathSciNetzbMATHGoogle Scholar
  6. Jiguang Sun (1987) Matrix perturbation analysis. Science Press, BeijingzbMATHGoogle Scholar
  7. Li C, Xie XP (2017) The DGM(1,1)atan arc-tangent function and its application. Syst Eng Theory Pract 37(12):3227–3234Google Scholar
  8. Li GD, Yamaguchi D, Nagai M (2007) A GM(1,1)–Markov chain combined model with an application to predict the number of Chinese international airlines. Technol Forecast Soc Chang 74(8):1465–1481CrossRefGoogle Scholar
  9. Li ML, Wang W, De G, Ji XH, Tan ZF (2018) Forecasting carbon emissions related to energy consumption in Beijing-Tianjin-Hebei region based on grey prediction theory and extreme learning machine optimized by support vector machine algorithm. Energies 11:2475–2489CrossRefGoogle Scholar
  10. Li C, Yang YJ, Liu SF (2019a) A new method to mitigate data fluctuations for time series prediction. Appl Math Model 65:390–407MathSciNetCrossRefGoogle Scholar
  11. Li C, Yang YJ, Liu SF (2019b) Comparative analysis of properties of weakening buffer operators in time series prediction models. Commun Nonlinear Sci Numer Simul 68:257–285MathSciNetCrossRefGoogle Scholar
  12. Li SY, Yang X, Li RR (2019c) Forecasting coal consumption in India by 2030:using linear modified linear (MGM-ARIMA) and linear modified nonlinear (BP-ARIMA) combined models. Sustaina bility 11:695–713CrossRefGoogle Scholar
  13. Lin YH, Chiu CC, Lee PC, Lin YJ (2012) Applying fuzzy grey modification model on inflow forecasting. Eng Appl Artif Intell 25(4):734–743CrossRefGoogle Scholar
  14. Liu JF, Liu SF, Fang ZG (2016) A class of new weakening buffer operators whose adjustable intensity can be changed and their applications. Chin J Manag Sci 24(8):172–176Google Scholar
  15. Lu JS, Xie WD, Zhou HB, Zhang AJ (2016) An optimized nonlinear grey Bernoulli model and its applications. Neurocomputing 177:206–214CrossRefGoogle Scholar
  16. Ma YS, Dai YZ (1993) Improvement of data generation method in grey system. Syst Sci Compr Stud Agric 9(2):113–116Google Scholar
  17. Ou SL (2012) Forecasting agricultural output with an improved grey forecasting model based on the genetic algorithm. Comput Electron Agric 85:33–39CrossRefGoogle Scholar
  18. Qian WY, Dang YG, Wang YM (2009) GM(1, 1) model based on weighting accumulated generating operation and its application. Math Pract Theory 39(15):47–51Google Scholar
  19. Song T (2004) The accumulated generating space. J Shandong Inst Archit Eng 19(1):88–90Google Scholar
  20. Song ZM, Deng JL (2001) The accumulated generating operation in opposite direction and its use in grey model GOM(1,1). Syst Eng 19(1):66–69MathSciNetGoogle Scholar
  21. Song Q, Wang AM (2009) Simulation and prediction of alkalinity in sintering process based on grey least squares support vector machine. J Iron Steel Res 16(5):1–6CrossRefGoogle Scholar
  22. Stewart GW (1977) On the perturbation of pseudo-inverses, projections and linear least squares problems. Slam Rev 19(4):634–662MathSciNetzbMATHGoogle Scholar
  23. Sun X, Sun WS, Wang JZ, Zhang YX, Gao YN (2016) Using a grey-Markov model optimized by Cuckoo search algorithm to forecast the annual foreign tourist arrivals to China. Tour Manag 52:369–379CrossRefGoogle Scholar
  24. Wang YH, Dang YG, Li YQ, Liu SF (2010) An approach to increase prediction precision of GM(1,1) model based on optimization of the initial condition. Expert Syst Appl 37(8):5640–5644CrossRefGoogle Scholar
  25. Wang QR, Liu L, Wang S, Wang JZ, Liu M (2017) Predicting Beijing’s tertiary industry with an improved grey model. Appl Soft Comput 57:482–494CrossRefGoogle Scholar
  26. Wu LF, Liu SF, Cui W, Liu DL, Yao TX (2014) Non-homogenous discrete grey model with fractional-order accumulation. Neural Comput Appl 25(5):1215–1221CrossRefGoogle Scholar
  27. Wu LF, Gao XH, Xiao YL, Yang YJ, Chen XN (2018) Using a novel multi-variable grey model to forecast the electricity consumption of Shandong province in China. Energy 157:327–335CrossRefGoogle Scholar
  28. Xu N, Dang YG (2018) Characteristic adaptive GM(1,1) model and forecasting of Chinese traffic pollution emission. Syst Eng Theory Pract 38(1):187–196Google Scholar
  29. Yang BH, Zhang ZQ (2003) The grey model has been accumulated generating operation in reciprocal number and its application. Math Pract Theory 33(10):21–26Google Scholar
  30. Zeng Bo (2017) Forecasting the relation of supply and demand of natural gas in China during 2015–2020 using a novel grey model. J Intell Fuzzy Syst 32(1):141–155CrossRefGoogle Scholar
  31. Zeng B, Li C (2016) Forecasting the natural gas demand in China using a self-adapting intelligent grey model. Energy 112:810–825CrossRefGoogle Scholar
  32. Zhao HR, Guo S (2016) An optimized grey model for annual power load forecasting. Energy 107:272–286CrossRefGoogle Scholar
  33. Zhou WJ, Zhang HR, Dang YG, Wang ZX (2017) New information priority accumulated grey discrete model and its application. Chin J Manag Sci 25(8):140–148Google Scholar

Copyright information

© Springer-Verlag GmbH Germany, part of Springer Nature 2019

Authors and Affiliations

  1. 1.College of Economics and ManagementHebei University of EngineeringHandanChina

Personalised recommendations