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A research on the grey prediction model GM(1,n). (English) Zbl 1266.62075

Grey system theory, initiated by J.L. Deng [Syst. Control Lett. 1, 288–294 (1982; Zbl 0482.93003)], is a methodology focusing on the study of problems involving uncertain information (see, e.g., S. Liu and Y. Lin, Grey systems. Theory and applications. Berlin: Springer (2010; Zbl 1222.93001)). The paper deals with a grey prediction model with a convolution integral, GMC(1,n), which is an improved version of the prediction model GM(1,n) (see Liu and Lin). The author applies the algorithm of the GMC(1,n) to explain why the existing GM(1,n) model is incorrect.

MSC:

62M20 Inference from stochastic processes and prediction
93B99 Controllability, observability, and system structure
93C99 Model systems in control theory
62M86 Inference from stochastic processes and fuzziness
65C60 Computational problems in statistics (MSC2010)
Full Text: DOI

References:

[1] Deng, J. L., Control problems of grey systems, System Control Letters, 1, 288-294 (1982) · Zbl 0482.93003
[2] Deng, J. L., Essential Topics on Grey Systems: Theory and Applications (1988), China Ocean Press: China Ocean Press Beijing
[3] Wang, Y., Compensation for the thermal error of a multi-axis machining center, Journal of Material Processing Technique, 75, 45-53 (1998)
[4] Guo, R., Modelling imperfectly repaired system data via grey differential equations with unequal-gapped times, Reliability Engineering and System Safety, 92, 378-391 (2007)
[5] Kung, L. M.; Yu, S. W., Prediction of index futures returns and the analysis of financial spillovers - A comparison between GARCH and the grey theorem, European Journal of Operational Research, 186, 1184-1200 (2008) · Zbl 1134.91032
[6] Pai, T. Y., Grey and neural network prediction of suspended solids and chemical oxygen demand in hospital wastewater treatment plant effluent, Computers and Chemical Engineering, 31, 1272-1281 (2007)
[7] Pai, T. Y.; Chiou, R. J.; Wen, H. H., Evaluating impact level of different factors in environmental impact assessment for incinerator plants using GM (1,N) model, Waste Management, 28, 1915-1922 (2008)
[8] Tien, T. L., The indirect measurement of tensile strength of material by the grey prediction model GMC \((1, n)\), Measurement Science Technology, 16, 1322-1328 (2005)
[9] Chen, C. K.; Tien, T. L., A new forecasting method for time continuous model of dynamic system, Applied Mathematics and Computation, 80, 225-244 (1996) · Zbl 0884.62101
[10] Chen, C. K.; Tien, T. L., A new transfer function model: the grey dynamic model GDM(2,2,1), International Journal of Systems Science, 27, 1371-1379 (1996) · Zbl 0878.93004
[11] Chen, C. K.; Tien, T. L., A new forecasting model GDM(2,2,1) of dynamic system, Proceedings of the Royal Society of London, Series A, 453, 879-896 (1997) · Zbl 0915.93059
[12] Chen, C. K.; Tien, T. L., The indirect measurement of tensile strength by the deterministic grey dynamic model DGDM(1,1,1), International Journal of Systems Science, 28, 683-690 (1997) · Zbl 0875.93031
[13] Chen, C. K.; Tien, T. L., A new forecasting method of discrete dynamic system, Applied Mathematics and Computation, 86, 61-84 (1997) · Zbl 0919.93007
[14] Tien, T. L.; Chen, C. K., The indirect measurement of fatigue limits of structural steel by the deterministic grey dynamic model DGDM (1,1,1), Applied Mathematical Modelling, 21, 611-619 (1997) · Zbl 0925.73004
[15] Tien, T. L.; Chen, C. K., Forecasting \(CO_2\) output from gas furnace by a new transfer function model GDM(2,2,1), Systems Analysis Modelling Simulation, 30, 265-287 (1998) · Zbl 0942.93501
[16] Tien, T. L., A research on the deterministic grey dynamic model with multiple inputs DGDMMI (1,1,1), Applied Mathematics and Computation, 139, 401-416 (2003) · Zbl 1036.93507
[17] Tien, T. L., A research on the prediction of machining accuracy by the deterministic grey dynamic model DGDM (1,1,1), Applied Mathematics and Computation, 161, 923-945 (2005) · Zbl 1122.93371
[18] Tien, T. L., The indirect measurement of tensile strength for a higher temperature by the new model IGDMC(1,n), Measurement, 41, 662-675 (2008)
[19] Tien, T. L., The deterministic grey dynamic model with convolution integral DGDMC(1,n), Applied Mathematical Modelling, 33, 3498-3510 (2009) · Zbl 1426.62278
[20] Tien, T. L., Forecasting \(CO_2\) output from gas furnace by grey prediction model IGMC(1,n), Journal of the Chinese Society of Mechanical Engineers, 31, 55-65 (2010)
[21] Su, C. R., Estimation for inner surface geometry of furnace wall using inverse process combined with grey prediction model, International Journal of Heat and Mass Transfer, 52, 3595-3605 (2009) · Zbl 1167.80403
[22] Wu, W. Y.; Chen, S. P., A prediction method using the grey model GMC(1,n) combined with the grey relational analysis a case study on Internet access population forecast, Applied Mathematics and Computation, 169, 198-217 (2005) · Zbl 1078.68549
[23] V O’Neil, P., Advanced Engineering Mathematics (2003), Brooks/Cole Publishing Company: Brooks/Cole Publishing Company NY
[24] Samuel, L. H., Metal Data (1952), Reinhold: Reinhold NJ
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