Using fractional order accumulation to reduce errors from inverse accumulated generating operator of grey model

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• 作者：Lifeng Wu (1)
  Sifeng Liu (1)
  Ligen Yao (2)
  Ruiting Xu (1)
  Xunping Lei (1)
  
  1. College of Economics and Management ; Nanjing University of Aeronautics and Astronautics ; Nanjing ; 210016 ; China
  2. School of Economics and Management ; Hebei University of Engineering ; Handan ; 056038 ; China
  
• 关键词：Grey system ; GM(2 ; 1) model ; Fractional order accumulation ; Tourism demand forecasting ; Deaths in road traffic accidents
• 刊名：Soft Computing - A Fusion of Foundations, Methodologies and Applications
• 出版年：2015
• 出版时间：February 2015
• 年：2015
• 卷：19
• 期：2
• 页码：483-488
• 全文大小：170 KB
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• 刊物类别：Engineering
• 刊物主题：Numerical and Computational Methods in Engineering
  Theory of Computation
  Computing Methodologies
  Mathematical Logic and Foundations
  Control Engineering
  
• 出版者：Springer Berlin / Heidelberg
• ISSN：1433-7479

文摘

To smooth the randomness, a grey forecasting model is formulated using the data of accumulating generation operator (AGO) rather than original data. Then the inverse accumulating generation operator (IAGO) is applied to find the predicted values of original data. It is proved that the errors from IAGO are affected by the order number of AGO. To achieve an accurate prediction, GM(2,1), which stands for one-variable and second-order differential equation, has been improved by means of fractional order AGO. Finally, four real data sets are imported for comparing the performance of the developed GM(2,1) with several other grey models, such as traditional GM(2,1) and GM(1,1). The simulation results show that optimized GM(2,1) has higher performances not only on model fitting but also on forecasting.