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**An extended grey forecasting model for omnidirectional forecasting considering data gap difference.**
*(English)*
Zbl 1228.62162

Summary: To achieve effective and efficient decision making in a highly competitive business environment, an enterprise must have an appropriate forecasting technique that can meet the requirements of both timeliness and accuracy. Accordingly, in the early stages, building a forecasting model with incomplete information and limited samples is very important to a business. Grey system theory is one of the prediction methods that can be built with a small sample and yet has a strong ability to make short-term predictions.

The purpose of this study is to come up with an improved forecasting model based on the concept of this theory to enlarge the applicability of the grey forecasting model in various situations. By extending the data transforming approach, this method generalizes a building procedure for the grey model to grasp the data outline and information trend. Specifically, a novel inverse accumulating generation operator is developed to enable omnidirectional forecasting. The research utilizes observations of the titanium alloy fatigue limit along with temperature changes as raw data to verify the performance of the proposed method. The experimental results show that not only can this method expand the application scope of the grey forecasting model, but also improve its forecasting accuracy.

The purpose of this study is to come up with an improved forecasting model based on the concept of this theory to enlarge the applicability of the grey forecasting model in various situations. By extending the data transforming approach, this method generalizes a building procedure for the grey model to grasp the data outline and information trend. Specifically, a novel inverse accumulating generation operator is developed to enable omnidirectional forecasting. The research utilizes observations of the titanium alloy fatigue limit along with temperature changes as raw data to verify the performance of the proposed method. The experimental results show that not only can this method expand the application scope of the grey forecasting model, but also improve its forecasting accuracy.

### MSC:

62P30 | Applications of statistics in engineering and industry; control charts |

90B50 | Management decision making, including multiple objectives |

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\textit{D.-C. Li} et al., Appl. Math. Modelling 35, No. 10, 5051--5058 (2011; Zbl 1228.62162)

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### References:

[1] | Deng, J.L., Control problems of grey systems, Syst. control lett., 1, 288-294, (1982) · Zbl 0482.93003 |

[2] | Chen, C.I.; Chen, H.L.; Chen, S.P., Forecasting of foreign exchange rates of taiwan’s major trading partners by novel nonlinear grey Bernoulli model NGBM(1,1), Commun. nonlinear sci. numer. simul., 13, 1194-1204, (2008) |

[3] | Huang, S.J.; Chiu, N.H.; Chen, L.W., Integration of the grey relational analysis with genetic algorithm for software effort estimation, Eur. J. oper. res., 188, 898-909, (2008) · Zbl 1144.90367 |

[4] | 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, Eur. J. oper. res., 186, 1184-1200, (2008) · Zbl 1134.91032 |

[5] | Li, D.C.; Chang, C.J.; Chen, C.C.; Chen, C.S., Using non-equigap grey model for small data set forecasting – a color filter manufacturing example, J. grey syst., 22, 375-382, (2010) |

[6] | Li, D.C.; Yeh, C.W.; Chang, C.J., An improved grey-based approach for early manufacturing data forecasting, Comput. ind. eng., 57, 1161-1167, (2009) |

[7] | Mao, M.Z.; Chirwa, E.C., Application of grey model GM(1,1) to vehicle fatality risk estimation, Technol. forecast. soc. chang., 73, 588-605, (2006) |

[8] | Shih, C.S.; Hsu, Y.T.; Yeh, J.; Lee, P.C., Grey number prediction using the grey modification model with progression technique, Appl. math. model., 35, 1314-1321, (2011) · Zbl 1211.62170 |

[9] | 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) |

[10] | Tien, T.L., The deterministic grey dynamic model with convolution integral DGDMC(1,n), Appl. math. model., 33, 3498-3510, (2009) · Zbl 1426.62278 |

[11] | Tsaur, R.C., Forecasting analysis by using fuzzy grey regression model for solving limited time series data, Soft comput., 12, 1105-1113, (2008) · Zbl 1142.62071 |

[12] | Tsaur, R.C.; Liao, Y.C., Forecasting LCD TV demand using the fuzzy grey model GM(1,1), Int. J. uncertainty fuzziness knowl.-based syst., 15, 753-767, (2007) |

[13] | Wu, C.R.; Chang, C.W.; Lin, H.L., A forecast model for evaluating physicians’ supply and demand in the taiwanese remote islands, J. grey syst., 21, 25-34, (2009) |

[14] | Xie, N.M.; Liu, S.F., Discrete grey forecasting model and its optimization, Appl. math. model., 33, 1173-1186, (2009) · Zbl 1168.62380 |

[15] | Xie, N.M.; Liu, S.F., Novel methods on comparing grey numbers, Appl. math. model., 34, 415-423, (2010) · Zbl 1185.68722 |

[16] | Yamaguchi, D.; Li, G.D.; Nagai, M., A grey-based rough approximation model for interval data processing, Inform. sci., 177, 4727-4744, (2007) · Zbl 1126.68613 |

[17] | Yao, T.X.; Liu, S.F.; Xie, N.M., On the properties of small sample of GM(1,1) model, Appl. math. model., 33, 1894-1903, (2009) · Zbl 1205.60085 |

[18] | Deng, J.L., The primary methods of grey system theory huazhong, (2005), Huazhong University of Science and Technology Press Wuhan, China |

[19] | He, X.G.; Sun, G.Z., A non-equigap grey model NGM(1,1), J. grey syst., 13, 189-192, (2001) |

[20] | Deng, J.L., Introduction to grey system theory, J. grey syst., 1, 1-24, (1989) · Zbl 0701.90057 |

[21] | Kang, X.Q.; Wei, Y., A new optimized method of non-equigap GM(1,1) model, J. grey syst., 20, 375-382, (2008) |

[22] | Callister, W.D.; Rethwisch, D.G., Fundamentals of materials science and engineering: an integrated approach, (2008), John Wiley & Sons New Jersey, United States |

[23] | Liu, S.F.; Lin, Y., Grey information: theory and practical applications, (2006), Springer London, Britain |

This reference list is based on information provided by the publisher or from digital mathematics libraries. Its items are heuristically matched to zbMATH identifiers and may contain data conversion errors. It attempts to reflect the references listed in the original paper as accurately as possible without claiming the completeness or perfect precision of the matching.