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Appl. Sci. 2016, 6(3), 73; doi:10.3390/app6030073

Evaluating Performance of the DGM(2,1) Model and Its Modified Models

Department of Industrial Engineering and Management, National Kaohsiung University of Applied Sciences, No. 415, Chien Kung Road, Sanmin District, Kaohsiung 80778, Taiwan
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Academic Editor: Yang Kuang
Received: 27 November 2015 / Revised: 22 February 2016 / Accepted: 24 February 2016 / Published: 4 March 2016
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Abstract

The direct grey model (DGM(2,1)) is considered for fluctuation characteristics of the sampling data in Grey system theory. However, its applications are quite uncommon in the past literature. The improvement of the precision of the DGM(2,1) is only presented in few previous researches. Moreover, the evaluation of forecasted performance of the DGM(2,1) model and its applications was not conducted in previous studies. As the results, this study aims to evaluate forecasted performance of the DGM(2,1) and its three modified models, including the Markov direct grey model MDGM(2,1), the Fourier direct grey model FDGM(2,1), and the Fourier Markov direct grey model FMDGM(2,1) in order to determine the application of the DGM(2,1) model in practical applications and academic research. The results demonstrate that the DGM(2,1) model has lower precision than its modified models, while the forecasted precision of the FDGM(2,1) is better than that of MDGM(2,1). Additionally, the FMDGM(2,1) model presents the best performance among all of the modified models of DGM(2,1), which can effectively overcome the fluctuating of the data sample and minimize the predicted error of the DGM(2,1) model. The finding indicated that the FMDGM(2,1) model does not only have advantages with regard to the sample size requirement, but can also be flexibly applied to the large fluctuation and random sequences with a high quality of estimation. View Full-Text
Keywords: DGM(2,1) model; Fourier series; Markov chain; MDGM(2,1); FDGM(2,1); FMDGM(2,1) model DGM(2,1) model; Fourier series; Markov chain; MDGM(2,1); FDGM(2,1); FMDGM(2,1) model
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. (CC BY 4.0).

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MDPI and ACS Style

Huang, Y.-F.; Wang, C.-N.; Dang, H.-S.; Lai, S.-T. Evaluating Performance of the DGM(2,1) Model and Its Modified Models. Appl. Sci. 2016, 6, 73.

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