Maximum entropy methods for weighted grey incidence analysis and applications

作者：Quan, Jing; Zeng, Bo^*; Wang, LuYun

来源：Grey Systems: Theory and Application , 2018, 8(2): 144-155.

DOI：10.1108/GS-12-2017-0047

• Grey incidence analysis
• Maximum entropy
• Weighted degree of grey incidence

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.

• 出版日期2018
• 单位重庆工商大学