Matrix form of interval multivariable gray model and its application
Grey Systems: Theory and Application
ISSN: 2043-9377
Article publication date: 4 May 2021
Issue publication date: 28 February 2022
Abstract
Purpose
The purpose of this paper is to make multivariable gray model to be available for the application on interval gray number sequences directly, the matrix form of interval multivariable gray model (IMGM(1,m,k) model) is constructed to simulate and forecast original interval gray number sequences in this paper.
Design/methodology/approach
Firstly, the interval gray number is regarded as a three-dimensional column vector, and the parameters of multivariable gray model are expressed in matrix form. Based on the dynamic gray action and optimized background value, the interval multivariable gray model is constructed. Finally, two examples and comparisons are carried out to verify the effectiveness of IMGM(1,m,k) model.
Findings
The model is applied to simulate and predict expert value, foreign direct investment, automobile sales and steel output, respectively. The results show that the proposed model has better simulation and prediction performance than another two models.
Practical implications
Due to the uncertainty information and continuous changing of reality, the interval gray numbers are used to characterize full information of original data. And the IMGM(1,m,k) model not only considers the characteristics of parameters changing with time but also takes into account information on lower, middle and upper bounds of interval gray numbers simultaneously to make better suitable for practical application.
Originality/value
The main contribution of this paper is to propose a new interval multivariable gray model, which considers the interaction between the lower, middle and upper bounds of interval numbers and need not to transform interval gray number sequences into real sequences. According to combining different characteristics of each bound of interval gray numbers, the matrix form of interval multivariable gray model is established to simulate and forecast interval gray numbers. In addition, the model introduces dynamic gray action to reflect the changes of parameters over time. Instead of white equation of classic MGM(1,m), the difference equation is directly used to solve the simulated and predicted values.
Keywords
Acknowledgements
This investigation was supported by the Science and Technology Innovation Fund of Henan Agricultural University (No. KJCX2020C01) and the Royal Society and NSFC (No. IEC\NSFC\170391\).
Citation
Guo, S., Jing, Y. and Li, B. (2022), "Matrix form of interval multivariable gray model and its application", Grey Systems: Theory and Application, Vol. 12 No. 2, pp. 318-338. https://doi.org/10.1108/GS-09-2020-0120
Publisher
:Emerald Publishing Limited
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