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Properties of the GM(1,1) with fractional order accumulation

Author

Listed:
  • Wu, Lifeng
  • Liu, Sifeng
  • Fang, Zhigeng
  • Xu, Haiyan

Abstract

For traditional grey model (GM(1,1)), it is proved theoretically that the initial condition is not utilized, and the simulative value is convex and increased or is the decreased and concave when the actual sequence is nonnegative increased. These shortcomings are the results of traditional first order accumulation on grey system model. However, for the GM(1,1) with fractional order accumulation, the initial condition is utilized, and the monotonicity and convexity of simulative value are uncertain when the actual value is nonnegative increased. The results of practical numerical examples demonstrate that the GM(1,1) with fractional order accumulation provides very remarkable predication performance compared with the traditional GM(1,1) model.

Suggested Citation

  • Wu, Lifeng & Liu, Sifeng & Fang, Zhigeng & Xu, Haiyan, 2015. "Properties of the GM(1,1) with fractional order accumulation," Applied Mathematics and Computation, Elsevier, vol. 252(C), pages 287-293.
    • Handle: RePEc:eee:apmaco:v:252:y:2015:i:c:p:287-293
    DOI: 10.1016/j.amc.2014.12.014
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    References listed on IDEAS

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    1. Li, Der-Chiang & Chang, Che-Jung & Chen, Chien-Chih & Chen, Wen-Chih, 2012. "Forecasting short-term electricity consumption using the adaptive grey-based approach—An Asian case," Omega, Elsevier, vol. 40(6), pages 767-773.
    2. Shun-Xiang Wu & De-Lin Luo & Zhi-Wen Zhou & Jian-Huai Cai & Yeu-Xiang Shi, 2011. "A kind of BP neural network algorithm based on grey interval," International Journal of Systems Science, Taylor & Francis Journals, vol. 42(3), pages 389-396.
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