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Multivariate grey gradient incidence model and its application

Ke Zhang (Business School, Hohai University, Nanjing, China)
Qiupin Zhong (Business School, Hohai University, Nanjing, China)
Yuan Zuo (Business School, Hohai University, Nanjing, China)

Grey Systems: Theory and Application

ISSN: 2043-9377

Article publication date: 7 August 2017




The purpose of this paper is to overcome the shortcomings of existing multivariate grey incidence models that cannot analyze the similarity of behavior matrixes.


First, the feasibility of using gradient to measure the similarity of continuous functions is analyzed theoretically and intuitively. Then, a grey incidence degree is constructed for multivariable continuous functions. The model employs the gradient to measure the local similarity, as incidence coefficient function, of two functions, and combines local similarity into global similarity, as grey incidence degree by double integral. Third, the gradient incidence degree model for behavior matrix is proposed by discretizing the continuous models. Furthermore, the properties and satisfaction of grey incidence atom of the proposed model are research, respectively. Finally, a financial case is studied to examine the validity of the model.


The proposed model satisfies properties of invariance under mean value transformation, multiple transformation and linear transformation, which proves it is a model constructed from similarity perspective. Meanwhile, the case study shows that proposed model performs effectively.

Practical implications

The method proposed in the paper could be used in financial multivariable time series clustering, personalized recommendation in e-commerce, etc., when the behavior matrixes need to be analyzed from trend similarity perspective.


It will promote the accuracy of multivariate grey incidence model.



The authors wish to thank anonymous referees and editors for their valuable review and comments on early drafts of this paper, and Dr Chen Hao and XiaoYongsheng for their contribution to this paper. Of course, authors are responsible for the paper seriously. The work was supported by the National Science and Technology Support Program of China under Grants No. 2015BAB07B01, National Natural Science Fund of China under Grants No. 71,401,052, Doctoral Fund of Ministry of Education of China under Grants No. 20,120,094,120,024, the Fundamental Research Funds for the Central Universities under Grant No. 2016B09214.


Zhang, K., Zhong, Q. and Zuo, Y. (2017), "Multivariate grey gradient incidence model and its application", Grey Systems: Theory and Application, Vol. 7 No. 2, pp. 236-246.



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