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

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Title: Absolute Degree of Grey Incidences for Matrix Sequence and Its Application.
Authors: Ke Zhang1 zhangke@nuaa.edu.cn, Qiuping Zhong1, Jingchun Feng1,2, Haiwei Zhou1,3,4, 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]
Copyright of Journal of Grey System is the property of Research Information Ltd. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Engineering Source
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DbLabel: Engineering Source
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  Data: Absolute Degree of Grey Incidences for Matrix Sequence and Its Application.
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  Data: <searchLink fieldCode="AR" term="%22Ke+Zhang%22">Ke Zhang</searchLink><relatesTo>1</relatesTo><i> zhangke@nuaa.edu.cn</i><br /><searchLink fieldCode="AR" term="%22Qiuping+Zhong%22">Qiuping Zhong</searchLink><relatesTo>1</relatesTo><br /><searchLink fieldCode="AR" term="%22Jingchun+Feng%22">Jingchun Feng</searchLink><relatesTo>1,2</relatesTo><br /><searchLink fieldCode="AR" term="%22Haiwei+Zhou%22">Haiwei Zhou</searchLink><relatesTo>1,3,4</relatesTo><br /><searchLink fieldCode="AR" term="%22Hui+Feng%22">Hui Feng</searchLink><relatesTo>1</relatesTo>
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  Data: <searchLink fieldCode="JN" term="%22Journal+of+Grey+System%22">Journal of Grey System</searchLink>. 2018, Vol. 30 Issue 1, p56-68. 13p.
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  Data: <searchLink fieldCode="DE" term="%22Gray+forecasting+model%22">Gray forecasting model</searchLink><br /><searchLink fieldCode="DE" term="%22Sequence+analysis%22">Sequence analysis</searchLink><br /><searchLink fieldCode="DE" term="%22Data+modeling%22">Data modeling</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models+of+decision+making%22">Mathematical models of decision making</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+models+of+forecasting%22">Mathematical models of forecasting</searchLink>
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  Label: Abstract
  Group: Ab
  Data: 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]
– Name: AbstractSuppliedCopyright
  Label:
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  Data: <i>Copyright of Journal of Grey System is the property of Research Information Ltd. and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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      – Code: eng
        Text: English
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        PageCount: 13
        StartPage: 56
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      – SubjectFull: Gray forecasting model
        Type: general
      – SubjectFull: Sequence analysis
        Type: general
      – SubjectFull: Data modeling
        Type: general
      – SubjectFull: Mathematical models of decision making
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      – SubjectFull: Mathematical models of forecasting
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            NameFull: Jingchun Feng
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            NameFull: Haiwei Zhou
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            NameFull: Hui Feng
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            – D: 01
              M: 01
              Text: 2018
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