G M (1,1) Optimization Model Re-Optimization

Abstract:

On the base of the basic differential equation, a new GM (1,1) model applying to non-homogenous index series was established by optimizing the background of original differential equation. Meanwhile, solution algorithm and efficiency of the optimization model was presented and verified in the paper respectively. The results showed that this nonlinear discrete gray prediction model significantly improves the simulation accuracy and is suitable for the non-homogeneous high-growth series. Therefore, our research has certain theory significance and the practical application value for simulation of grey model.

• Periodical: Advanced Materials Research (Volumes 538-541)
• Pages: 2543-2547
• DOI: https://doi.org/10.4028/www.scientific.net/AMR.538-541.2543
• Online since: June 2012
• Authors: Yao Chen
• Keywords: Background Value, GM(1,1), Non-Homogenous Index Series, Optimization, Restore Value

References

[1] J. Deng: Estimate and Decision of Grey System (Huazhong University of Science& Technology Publications, Wuhan 2002). (In Chinese).

[2] S. Liu and J. Deng: The range suitable for GM (1, 1). System Engineering–Theory & Practice 5, (2000), pp.121-124. (In Chinese).

[3] L. Lv and W. Wu: Research on the optimization of grey model GM (1, 1). System Engineering –Theory & Practice 8, (2001), pp.92-96. (In Chinese).

[4] D. Luo, S. Liu and Y. Dang: The optimization of grey model GM (1, 1). Engineering Science Vol. 8 (2003), pp.50-53. (In Chinese).

[5] P. Zhou and Y. Wei: The Optimization of Background Value in Grey Model GM (1, 1). Journal of Grey System 9 (2006), pp.139-142.

[6] H. Xue and Y. Wei: A Transformation Based on Grey Differential Equation Matching with White Differential Equation Even More. The Journal of Grey System 3(2008).

[7] Y. Wang, W. Li, B. Wang and M. Chen: The Modeling Method of GM (1, 1) with a Step by Step Optimum Grey Derivative's Whiting Values. System Engineering –Theory & Practice 9 (2002), pp.128-131.

[8] G. Tan: The structure method and application of background value in grey system GM(1, 1) model (I). Systems Engineering-theory & Practice 4(2000), pp.98-103. (In Chinese).

[9] T. Yao and S. Liu: Improvement of a Forecasting Discrete GM (1, 1). System's Engineering 9 (2007), pp.103-106. (In Chinese).

[10] D. Yu and Y. Wei: The new method of determining the development Coefficient and the initial value of prediction models. Statistics and Decision2 (2008), pp.42-44. (In Chinese).

[11] D. Yu and Y. Wei, in: 16th Workshop On Grey System Theory and its Applications(2008), pp.440-447. (In Chinese).

[12] Y. Zhang, Y. Wei, in: Proceeding of the 2008 IEEE International Conference on Systems, Man, and Cybernetics (2008). (EI index).

[13] N. Xie and S. Liu: Research on the non-homogenous discrete grey model and its parameter's properties. Systems Engineering and Electronics5 (2008), pp.863-867. (In Chinese).