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Mathematical Problems in Engineering
Volume 2015, Article ID 740272, 7 pages
Research Article

An Improved Nonlinear Grey Bernoulli Model Combined with Fourier Series

Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, 415 Chien-Kung Road, Kaohsiung 807, Taiwan

Received 28 April 2015; Revised 3 August 2015; Accepted 12 August 2015

Academic Editor: Meng Du

Copyright © 2015 Wang Chia-Nan and Phan Van-Thanh. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


Grey forecasting is a dynamic forecasting model and has been widely used in various fields. In recent years, many scholars have proposed new procedures or new models to improve the precision accuracy of grey forecasting for the fluctuating data sets. However, the prediction accuracy of the grey forecasting models existing may not be always satisfactory in different scenario. For example, the data are highly fluctuating are with lots of noise. In order to deal with this issue, a Fourier Nonlinear Grey Bernoulli Model (1, 1) (abbreviated as F-NGBM (1, 1)) is proposed to enhance the forecasting performance. The proposed model was established by using Fourier series to modify the residual errors of Nonlinear Grey Bernoulli Model (1, 1) (abbreviated as (NGBM (1, 1)). To verify the effectiveness of the proposed model, fluctuation data of the numerical example in Wang et al.’s paper (Wang et al. 2011) and practical application are used. Both of these simulation results demonstrate that the proposed model could forecast more precisely than several different kinds of grey forecasting models. For future direction, this proposed model can be applied to forecast the performance with the high fluctuation data in the different industries.