A grey-based fitting coefficient to build a hybrid forecasting model for small data sets.

*(English)*Zbl 1252.62118Summary: In the current rapidly changing manufacturing conditions, controlling manufacturing systems effectively and efficiently is a critical issue for enterprises, especially in their early stages. However, it is often difficult to make correct decisions, with the insufficient information available at such times. We thus develop a two-stage modeling procedure to build a predictive model using few samples. We first use three conventional approaches to establish forecasting models, and then implement pre-testing with the proposed grey-based fitness measuring index to determine the weights to create a hybrid model. Two data sets, including color filter manufacturing data and the Asia-Pacific Economic Cooperation energy data base, are evaluated in the experiment, and the results show that the proposed method not only has good forecasting performance, but also reduces the influence forecasting errors. Accordingly, the proposed procedure is thus considered a feasible approach for small-data-set forecasting.

##### MSC:

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

62M20 | Inference from stochastic processes and prediction |

62P20 | Applications of statistics to economics |

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\textit{D.-C. Li} et al., Appl. Math. Modelling 36, No. 10, 5101--5108 (2012; Zbl 1252.62118)

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##### References:

[1] | Huang, C.F.; Moraga, C., A diffusion-neural-network for learning from small samples, Int. J. approx. reas., 35, 137-161, (2004) · Zbl 1068.68120 |

[2] | Lin, Y.S.; Li, D.C., The generalized-trend-diffusion modeling algorithm for small data sets in the early stages of manufacturing systems, Eur. J. oper. res., 207, 121-130, (2010) |

[3] | Tsai, T.I.; Li, D.C., Utilize bootstrap in small data set learning for pilot run modeling of manufacturing systems, Exp. syst. appl., 35, 1293-1300, (2008) |

[4] | Li, D.C.; Yeh, C.W., A non-parametric learning algorithm for small manufacturing data sets, Exp. syst. appl., 34, 391-398, (2008) |

[5] | Li, D.C.; Lin, Y.S., Learning management knowledge for manufacturing systems in the early stages using time series data, Eur. J. oper. res., 184, 169-184, (2008) · Zbl 1153.91796 |

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

[7] | Kose, W.; Temiz, I.; Erol, S., Grey system approach for economic order quantity models under uncertainty, J. grey syst., 23, 71-82, (2011) |

[8] | Li, D.C.; Chang, C.J.; Chen, W.C.; Chen, C.C., An extended grey forecasting model for omnidirectional forecasting considering data gap difference, Appl. math. model., 35, 5051-5058, (2011) · Zbl 1228.62162 |

[9] | Li, G.D.; Masuda, S.; Yamaguchi, D.; Nagai, M., The optimal gnn-pid control system using particle swarm optimization algorithm, Int. J. innov. comput. inf. control, 5, 3457-3469, (2009) |

[10] | 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 |

[11] | 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) |

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

[13] | Wang, Z.X.; Hipel, K.W.; Wang, Q.; He, S.W., An optimized NGBM(1,1) model for forecasting the qualified discharge rate of industrial wastewater in China, Appl. math. model., 35, 5524-5532, (2011) |

[14] | 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 |

[15] | Zhu, J.M.; Wang, J.; Lei, J.T., Grey predictive control of stress on trauma section during union of fracture, J. grey syst., 23, 15-24, (2011) |

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

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

[18] | Witten, I.H.; Frank, E., Data mining: practical machine learning tools and techniques, (2005), Morgan Kaufmann Publishers San Francisco, United States · Zbl 1076.68555 |

[19] | Hu, M.Y.; Zhang, G.Q.; Jiang, C.Z.; Patuwo, B.E., A cross-validation analysis of neural network out-of-sample performance in exchange rate forecasting, Decis. sci., 30, 197-216, (1999) |

[20] | Yokum, J.T.; Armstrong, J.S., Beyond accuracy: comparison of criteria used to select forecasting methods, Int. J. forecast., 11, 591-597, (1995) |

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.