Maximum entropy methods for weighted grey incidence analysis and applications
Abstract
Purpose
Equally weighted factors and initial data from behavioural sequences are used for calculating the degree of grey incidence in Deng’s grey incidence analysis. However, certain grey information cannot be directly obtained, and the correlation coefficients of each sequence at different times are of different importance to the system. The purpose of this paper is to propose an improved grey incidence model with new grey incidence coefficients and weighted degree of grey incidence. Some grey information can be obtained more easily by using the grey transformation sequences, and the maximum entropy method is used to calculate the weights of new grey incidence coefficients, so the new degree of grey incidence was distinguished more effectively by the proposed model.
Design/methodology/approach
New grey incidence coefficients are defined using transformation sequences of the initial data. To overcome the shortcomings arising from the use of equal weights, the maximum entropy method is proposed for determining the weights of the grey incidence coefficients. The resulting model optimises the classical models and evaluates the influencing factors more effectively. The effectiveness of the model was verified by a numerical example. Furthermore, the model was used for analysing the main influencing factors of the tertiary industry in China.
Findings
The proposed model optimises the classical models, and the application example shows that urbanisation has the greatest effect on employment in the tertiary sector.
Originality/value
An improved grey incidence model is proposed that improves the grey incidence coefficients and their weights, and has better performance than the classical models. The model was successfully used in the analysis of the influence factors of the tertiary industry in China. The results indicate that the model can reflect the significance of incidence coefficients at different time points; therefore, their fluctuation can be effectively controlled.
Keywords
Acknowledgements
The authors’ work was supported by National Natural Science Foundation of China (No. 71771033 and No. 71271226), Chongqing Municipal Social Science Planning Commission Project of China (2016WT37), Science and Technology Research Project of Chongqing Education Commission (KJ1706166) and the open research fund of Chongqing Key Laboratory of Electronic Commerce Supply Chain System (1456026), also by 2017 annual PhD project of Rongzhi College of Chongqing Technology and Business University.
Citation
Quan, J., Zeng, B. and Wang, L. (2018), "Maximum entropy methods for weighted grey incidence analysis and applications", Grey Systems: Theory and Application, Vol. 8 No. 2, pp. 144-155. https://doi.org/10.1108/GS-12-2017-0047
Publisher
:Emerald Publishing Limited
Copyright © 2018, Emerald Publishing Limited