Abstract
Grey models are built on the basis of the real number series, not the fuzzy number series. In this paper, GM (1, 1), a basic prediction model of grey models, is generalized to the fuzzy number series. GM (1, 1) based on interval fuzzy number series [IFGM (1, 1)] is proposed firstly, which is suitable for the prediction of interval number series with weak fluctuation. In order to extend its applicable range, a revised model is then proposed. Markov prediction theory is applied to revising IFGM (1, 1) to make it suitable for the fluctuating interval number series. The general development tendency of the raw series is embodied by grey model and the random fluctuation is reflected by Markov prediction. The first practical example has shown IFGM (1, 1) is effective for small sample and weak fluctuating series. The consumer price indexes of China from 1996 to 2009 are taken as an example of fluctuating interval number series. Revised IFGM (1, 1), IFGM (1, 1), double exponential smoothing method and autoregressive moving average (ARMA) are all applied to it. Comparison of the results has shown the revised IFGM (1, 1)has the best precision than the other models.
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Acknowledgments
This research is supported by the National Science Foundation of China (No.11071178 and No.11162004) and the Research Foundation of Humanity and Social Science of Ministry of Education of China (No.11YJAZH131). Authors would like to thank referees for their helpful comments.
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Zeng, Xy., Shu, L., Huang, Gm. (2014). A Revised Grey Model for Fluctuating Interval Fuzzy Series Forecasting. In: Cao, BY., Nasseri, H. (eds) Fuzzy Information & Engineering and Operations Research & Management. Advances in Intelligent Systems and Computing, vol 211. Springer, Berlin, Heidelberg. https://doi.org/10.1007/978-3-642-38667-1_24
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DOI: https://doi.org/10.1007/978-3-642-38667-1_24
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