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AIMS Mathematics

2023, Volume 8, Issue 7: 15993-16012. doi: 10.3934/math.2023816
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A new method for parameter estimation of extended grey GM(2, 1) model based on difference equation and its application

  • School of Mathematical Sciences, Suzhou University of Science and Technology, Suzhou 215009, China
  • Received: 24 February 2023 Revised: 24 April 2023 Accepted: 25 April 2023 Published: 04 May 2023

  • MSC : 65Q10, 34K60, 34M30, 39A10

  • The common models used for grey system predictions include the GM(1, 1), the GM(N, 1), the GM(1, N) and so on, in which the GM(N, 1) model is an important type. Especially, the GM(2, 1) model is used widely, but it shows low modeling precision sometimes because of the improper parameter estimation method. To improve the model's precision, the paper proposes an extended grey GM(2, 1) model and gives a new parameter estimation method for the extended GM(2, 1) model based on the difference equation. The paper builds eight different grey models for the example. Results show that the improved method proposed has the highest precision. The method proposed can improve the popularization and application of the grey GM(N, 1) model.

    Citation: Maolin Cheng. A new method for parameter estimation of extended grey GM(2, 1) model based on difference equation and its application[J]. AIMS Mathematics, 2023, 8(7): 15993-16012. doi: 10.3934/math.2023816

    Related Papers:

  • The common models used for grey system predictions include the GM(1, 1), the GM(N, 1), the GM(1, N) and so on, in which the GM(N, 1) model is an important type. Especially, the GM(2, 1) model is used widely, but it shows low modeling precision sometimes because of the improper parameter estimation method. To improve the model's precision, the paper proposes an extended grey GM(2, 1) model and gives a new parameter estimation method for the extended GM(2, 1) model based on the difference equation. The paper builds eight different grey models for the example. Results show that the improved method proposed has the highest precision. The method proposed can improve the popularization and application of the grey GM(N, 1) model.


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