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Article

An optimized conformable fractional non-homogeneous gray model and its application

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Pages 5988-6003 | Received 26 Oct 2019, Accepted 22 Jun 2020, Published online: 04 Jul 2020

References

  • Andrieu, C., A. Doucet, and R. Holenstein. 2010. Particle Markov chain Monte Carlo methods. Journal of the Royal Statistical Society: Series B (Statistical Methodology) 72 (3):269–342. doi:10.1111/j.1467-9868.2009.00736.x.
  • Cui, J., S-f Liu, B. Zeng, and N-m Xie. 2013. A novel grey forecasting model and its optimization. Applied Mathematical Modelling 37 (6):4399–406. doi:10.1016/j.apm.2012.09.052.
  • Deng, J. L. 1982. Control problems of grey systems. Systems & Control Letters 1:288–94.
  • Ding, S., K. W. Hipel, and Y-g Dang. 2018. Forecasting china’s electricity consumption using a new grey prediction model. Energy 149:314–28. doi:10.1016/j.energy.2018.01.169.
  • Eberhart, R., and J. Kennedy. 1995. Particle swarm optimization. In Proceedings of the IEEE International Conference on Neural Networks, 1942–8. Citeseer volume 4.
  • Goldberger, A. S. 1962. Best linear unbiased prediction in the generalized linear regression model. Journal of the American Statistical Association 57 (298):369–75. doi:10.1080/01621459.1962.10480665.
  • Golub, G. H., and C. F. Van Loan. 1996. Matrix computations, 3rd ed. vol. 3. Baltimore, MD: JHU press.
  • Hamzacebi, C., and H. A. Es. 2014. Forecasting the annual electricity consumption of turkey using an optimized grey model. Energy 70:165–71. doi:10.1016/j.energy.2014.03.105.
  • Hassoun, M. H. 1995. Fundamentals of artificial neural networks. Cambridge, MA: MIT press.
  • Khalil, R., H. M. Al, A. Yousef, and M. Sababheh. 2014. A new definition of fractional derivative. Journal of Computational and Applied Mathematics 264:65–70. doi:10.1016/j.cam.2014.01.002.
  • Kumar, U., and V. Jain. 2010. Time series models (grey-Markov, grey model with rolling mechanism and singular spectrum analysis) to forecast energy consumption in India. Energy 35 (4):1709–16. doi:10.1016/j.energy.2009.12.021.
  • Lin, C.-T., and S.-Y. Yang. 2003. Forecast of the output value of Taiwan’s opto-electronics industry using the grey forecasting model. Technological Forecasting and Social Change 70 (2):177–86. doi:10.1016/S0040-1625(01)00191-3.
  • Liu, X., and N. Xie. 2019. A nonlinear grey forecasting model with double shape parameters and its application. Applied Mathematics and Computation 360:203–12. doi:10.1016/j.amc.2019.05.012.
  • Ma, X., and Z-b Liu. 2018. The kernel-based nonlinear multivariate grey model. Applied Mathematical Modelling 56:217–38. doi:10.1016/j.apm.2017.12.010.
  • Ma, X., W. Wu, B. Zeng, Y. Wang, and X. Wu. 2020. The conformable fractional grey system model. ISA Transactions 96:255–71. doi:10.1016/j.isatra.2019.07.009.
  • Mao, M., and E. C. Chirwa. 2006. Application of grey model gm (1, 1) to vehicle fatality risk estimation. Technological Forecasting and Social Change 73 (5):588–605. doi:10.1016/j.techfore.2004.08.004.
  • Noble, W. S. 2006. What is a support vector machine? Nature Biotechnology 24 (12):1565–7. doi:10.1038/nbt1206-1565.
  • Sowell, F. 1992. Modeling long-run behavior with the fractional arima model. Journal of Monetary Economics 29 (2):277–302. doi:10.1016/0304-3932(92)90016-U.
  • Wang, Z.-X., L.-Y. He, and H.-H. Zheng. 2019. Forecasting the residential solar energy consumption of the United States. Energy 178:610–23. doi:10.1016/j.energy.2019.03.183.
  • Wang, Z.-X., Q. Li, and L.-L. Pei. 2017. Grey forecasting method of quarterly hydropower production in china based on a data grouping approach. Applied Mathematical Modelling 51:302–16. doi:10.1016/j.apm.2017.07.003.
  • Wang, Z.-X., Q. Li, and L.-L. Pei. 2018. A seasonal gm (1, 1) model for forecasting the electricity consumption of the primary economic sectors. Energy 154:522–34. doi:10.1016/j.energy.2018.04.155.
  • Wei, M., Z. Bo, L. Si-Feng, and F. Zhi-Geng. 2015. Study on expansion and properties of grey accumulating generation operator. In 2015 IEEE International Conference on Grey Systems and Intelligent Services (GSIS), 61–65. doi:10.1109/GSIS.2015.7301827.
  • Wu, L., S. Liu, L. Yao, S. Yan, and D. Liu. 2013. Grey system model with the fractional order accumulation. Communications in Nonlinear Science and Numerical Simulation 18 (7):1775–85. doi:10.1016/j.cnsns.2012.11.017.
  • Wu, L.-F., S.-F. Liu, W. Cui, D.-L. Liu, and T.-X. Yao. 2014. Non-homogenous discrete grey model with fractional-order accumulation. Neural Computing and Applications 25 (5):1215–21. doi:10.1007/s00521-014-1605-1.
  • Wu, W.,. X. Ma, Y. Zhang, W. Li, and Y. Wang. 2020. A novel conformable fractional non-homogeneous grey model for forecasting carbon dioxide emissions of BRICS countries. The Science of the Total Environment 707:135447. doi:10.1016/j.scitotenv.2019.135447.
  • Wu, W-z, and T. Zhang. 2020. An improved gray interval forecast method and its application. Communications in Statistics - Theory and Methods 49 (5):1120–31. doi:10.1080/03610926.2018.1554132.
  • Xie, N., and S. Liu. 2005. Discrete gm (1, 1) and mechanism of grey forecasting model. Systems Engineering-Theory & Practice 1:93–9.
  • Xie, N-m, and S-f Liu. 2009. Discrete grey forecasting model and its optimization. Applied Mathematical Modelling 33 (2):1173–86. doi:10.1016/j.apm.2008.01.011.
  • Xie, W., C. Liu, and W.-Z. Wu. 2020. The fractional non-equidistant grey opposite-direction model with time-varying characteristics. Soft Computing 24 (9):6603–12. doi:10.1007/s00500-020-04799-7.
  • Zeng, B., H. Duan, and Y. Zhou. 2019. A new multivariable grey prediction model with structure compatibility. Applied Mathematical Modelling 75:385–97. doi:10.1016/j.apm.2019.05.044.

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