Absolute Degree of Grey Incidences for Matrix Sequence and Its Application.

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Bibliographic Details
Title:	Absolute Degree of Grey Incidences for Matrix Sequence and Its Application.
Authors:	Ke Zhang¹ zhangke@nuaa.edu.cn, Qiuping Zhong¹, Jingchun Feng^1,2, Haiwei Zhou^1,3,4, Hui Feng¹
Source:	Journal of Grey System. 2018, Vol. 30 Issue 1, p56-68. 13p.
Subjects:	Gray forecasting model, Sequence analysis, Data modeling, Mathematical models of decision making, Mathematical models of forecasting
Abstract:	To extend the grey incidence analysis theory into multi-dimension space, a new absolute degree of grey incidences for matrix sequence data was proposed. Firstly, the data structure of the matrix sequence was analyzed, the matrix sequence of a system behavior was formally defined, and the starting zeroing operator for time series is extended for matrix sequence. Secondly, regular hexahedral data model commonly used in geology was introduced to shape the spatial geometrical features of behavioral matrix sequence. With the method, the definition of matrix sequence data volume was proposed, and the similarity measure of two factors was transformed into proximity measure of two data volumes. Thirdly, the traditional absolute degree of grey incidences was employed to analyze the relationship of two matrix sequences, and its parameters were recomputed by the triple integral in the multi-dimension space. In addition, its properties were reproofed. The properties indicated the model satisfied the axioms of grey incidence analysis and translation invariance. Therefore, the model belonged to the proximity grey incidences model. Lastly, the market segmentation of a bicycle company is studied by the proposed model with the multidimensional data model constructed by its marketing department. The result shows that the proposed model was feasible and efficient. [ABSTRACT FROM AUTHOR]
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Database:	Engineering Source

Description
Abstract:	To extend the grey incidence analysis theory into multi-dimension space, a new absolute degree of grey incidences for matrix sequence data was proposed. Firstly, the data structure of the matrix sequence was analyzed, the matrix sequence of a system behavior was formally defined, and the starting zeroing operator for time series is extended for matrix sequence. Secondly, regular hexahedral data model commonly used in geology was introduced to shape the spatial geometrical features of behavioral matrix sequence. With the method, the definition of matrix sequence data volume was proposed, and the similarity measure of two factors was transformed into proximity measure of two data volumes. Thirdly, the traditional absolute degree of grey incidences was employed to analyze the relationship of two matrix sequences, and its parameters were recomputed by the triple integral in the multi-dimension space. In addition, its properties were reproofed. The properties indicated the model satisfied the axioms of grey incidence analysis and translation invariance. Therefore, the model belonged to the proximity grey incidences model. Lastly, the market segmentation of a bicycle company is studied by the proposed model with the multidimensional data model constructed by its marketing department. The result shows that the proposed model was feasible and efficient. [ABSTRACT FROM AUTHOR]
ISSN:	09573720