A greyness reduction framework for prediction of grey heterogeneous data
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METHODOLOGIES AND APPLICATION
A greyness reduction framework for prediction of grey heterogeneous data Chong Li1,2 • Yingjie Yang2 • Sifeng Liu3
Ó Springer-Verlag GmbH Germany, part of Springer Nature 2020
Abstract Existing operational rules of interval grey numbers do not make full use of possible background information when determining the interval boundaries, and this may result in inconsistent results if applying different logical operations. This paper finds that multiplication and division rules of interval grey numbers do not meet the calculation rule of inverse operators. Direct solution and inverse solution of the same interval grey number object may differ not only in numerical ranges but also in greyness degrees. To improve the accuracy of grey number calculation, new operational rules for multiplication and division of interval grey numbers are proposed. Then the traditional prediction modelling method of grey heterogeneous data is refined and expanded by integrating a greyness reduction preprocessing, which is based on the proposed calculation rules. Application of the expanded heterogeneous interval grey number prediction model to a stock replenishment scheduling problem in emergency rescue scenarios is included to illustrate the new operational rules of grey numbers and their application in prediction algorithm, and the proposed approach is compared with other existing methods to demonstrate its effectiveness. Keywords Operational rule Greyness reduction Grey interval number Prediction model Stock replenishment scheduling
1 Introduction Grey prediction is an important part of the grey system theory. As an emerging decision-making tool for system evolution estimations or predictions, grey prediction theory has caught the attention of scholars and practitioners from various disciplines and been utilized in a wide variety of
Communicated by V. Loia. & Chong Li [email protected] Yingjie Yang [email protected] Sifeng Liu [email protected] 1
School of Economics and Management, Fuzhou University, 2 Xue Yuan Rd., University Town, Fuzhou 350108, China
2
Centre for Computational Intelligence, De Montfort University, Leicester LE1 9BH, UK
3
College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
fields (Wu et al. 2015; Liu and Forrest 2010). The main objectives of current researches related to grey prediction are: 1. The extension and modification of the classic GM(1, 1) model and their practical applications (Tsaur 2008, 2009; Xie and Liu 2005). 2. The improvement in the background information and raw data used in developing a prediction model (Evans 2014; Li et al. 2015; Wu et al. 2016). 3. Comparative assessment of grey model-based methods and common time series forecasting methods in different application fields (Bezuglov and Comert 2016). 4. The combinations of grey models and other theoretical models to improve the accuracy of predictions (Guo et al. 2015; Ogiela et al. 2014; Wu et al. 2
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