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Discrete grey forecasting model and its optimization. (English) Zbl 1168.62380
Summary: Although the grey forecasting model has been successfully adopted in various fields and demonstrated promising results, the literatures show its performance could be further improved. For this purpose, this paper proposes a novel discrete grey forecasting model termed DGM model and a series of optimized models of DGM. This paper modifies the algorithm of $$GM(1, 1)$$ model to enhance the tendency catching ability. The relationship between the two models and the forecasting precision of the DGM model based on the pure index sequence is discussed. Further studies on three basic forms and three optimized forms of the DGM model are also discussed. As shown in the results, the proposed model and its optimized models can increase the prediction accuracy. When the system is stable approximately, DGM model and the optimized models can effectively predict the developing system. This work contributes significantly to improve grey forecasting theory and proposes more novel grey forecasting models.

##### MSC:
 62M20 Inference from stochastic processes and prediction 62M99 Inference from stochastic processes
##### Keywords:
discrete; pure index sequence; accumulating generation
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##### References:
 [1] Liu, S.F.; Lin, Y., Grey information theory and practical applications, (2006), Springer-Verlag London [2] Pawlak, Z., Rough sets, Int. J. inform. comp. sci., 11, 341-356, (1982) · Zbl 0501.68053 [3] Pawlak, Z.; Grzymala-Busse, J.W.; Slowinski, R., Rough sets, Commun. ACM, 38, 11, 89-95, (1995) [4] Zadeh, L.A., Fuzzy sets, Inform. control, 8, 338-353, (1965) · Zbl 0139.24606 [5] Deng, J.L., The control problem of grey systems, Syst. control lett., 1, 5, 288-294, (1982) · Zbl 0482.93003 [6] Lin, Y.; Liu, S.F., A systemic analysis with data, Int. J. general syst., 29, 6, 1001-1013, (2000) · Zbl 0980.62103 [7] Liu, S.F.; Forrest, J., The role and position of grey systems theory in science development, J. grey syst., 9, 4, 351-356, (1997) [8] Deng, J.L., Introduction to grey system theory, J. grey syst., 1, 1, 1-24, (1989) · Zbl 0701.90057 [9] Deng, J.L., The basis of grey theory, (2002), Press of Huazhong University of Science & Technology Wuhan, China [10] Deng, J.L., Grey prediction and grey decision, (2002), Press of Huazhong University of Science & Technology Wuhan, China [11] Mu, Y., An unbiased GM(1,1) model with optimum grey derivative’s whitening values, Math. pract. theory, 33, 3, 13-16, (2003), (in Chinese) [12] Wang, Y.N.; Liu, K.D., GM(1,1) modeling method of optimum the whiting values of grey derivative, Syst. eng. theory pract., 21, 5, 124-128, (2001) [13] Song, Z.M.; Tong, X.J.; Xiao, X.P., Center approach grey GM(1,1) model, Syst. eng. theory pract., 21, 5, 110-113, (2001) [14] Tan, G.J., The structure method and application of background value in grey system GM(1,1) model, Syst. eng. theory pract., 20, 4, 99-103, (2000) [15] Liu, B.; Liu, S.F., Optimum time response sequence for GM(1,1), Chinese J. manage. sci., 11, 4, 54-57, (2003) [16] Luo, D.; Liu, S.F.; Dang, Y.G., The optimization of grey model GM(1,1), Chinese eng. sci., 5, 8, 50-53, (2003) [17] Zhang, H.; Hu, S.G., Accurate solution for GM(1,1) model, Syst. eng.—theory methodol. appl., 10, 1, 72-74, (2001) [18] Lin, Y.-H.; Lee, P.-C., Novel high-precision grey forecasting model, Automat. constr., (2007) [19] Liu, S.F.; Deng, J.L., The range suitable for GM(1,1), Syst. eng. theory pract., 21, 5, 121-124, (2000)
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