ABSTRACT Applying the reciprocal accumulated generating and the reconstruction method of GRM(1,1) model’s background value of non-equidistant sequence based on the exponential trait of grey model and the definition of integral for the problem of lower precision as well as lower adaptability in non-equidistant GM(1,1) model, the calculation formulas were deduced and a novel non-equidistant GRM(1,1) model generated by reciprocal accumulated generating was put forward. The grey GRM(1,1) model can be used in non-equidistant interval & equidistant interval time series and has the characteristic of high precision as well as high adaptability. Example validates the practicability and reliability of the proposed model.
Cite this paper
R. Zou, "A Novel Non-Equidistant Grey GRM(1,1) Model Based on Reciprocal Accumulated Generating," Applied Mathematics, Vol. 3 No. 8, 2012, pp. 910-913. doi: 10.4236/am.2012.38135.
 Y. X. Luo, L. T. Zhang and M. Li, “Grey Systems and Applications in Mechanical Engineering,” National University of Defense Technology Press, Changsha, 2001.
 Y. X. Luo and J. R. Zhou, “Non-Equidistance GM(1,1) Model and Its Application in Fatigue Experimental Data Processing and On-Line Control,” Journal of Mechanical Strength, Vol. 18, No. 3,1996, pp. 60-63.
 Y. X. Luo, X. Wu and M. Li, “Function-Transfer Method of Parameters Estimation Of Grey GM(1,1) Model and Its Application,” Journal of Mechanical Strength, Vol. 24, No. 3, 2002, pp. 450-452.
 W. Z. Dai and J. F. Li, “Modeling Research on Non-Equidistance GM(1,1) Model,” Systems Engineering Theory & Practice, Vol. 25, No. 9, 2005, pp. 89-93 .
 F. X. Wang, “Improvement on Unequal Interval Gray Forecast Model,” Fuzzy Information and Engineering, Vol. 6, No. 1, 2006, pp.118-123.
 Y. M. Wang, Y. G. Dang and Z. X. Wang, “The Optimization of Background Value in Non-Equidistant GM(1,1) Model,” Chinese Journal of Management Science, Vol. 16, No. 4, 2008, pp. 159-162 .
 Z. M. Song and J. L. Deng, “The Accumulated Generating Operation in Opposite Direction and Its Use in Grey Model GOM(1,1),” Systems Engineering, Vol. 19, No. 1, 2001, pp. 66-69.
 B. H. Yang and Z. Q. Zhang, “The Grey Model Has Been Accumulated Generating Operation in Reciprocal Number and Its Application,” Mathematics in Practice and Theory, Vol. 33, No. 10, 2003, pp. 21-25.
 H. Zhou and X. G. Wang, “A Improvement of the Grey Model GRM(1,1) Generated by Accumulation Generating Operation of Reciprocal Number,” Journal of Shenyang Ligong University, Vol. 27, No. 4, 2008, pp. 84-86.
 D. Y. Xue and Y. Q. Chen, “Solving Applied Mathematical Problems with Matlab,” CRC Press, Inc., Outside North America, 2009.