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A summary on the research of GRA models

A summary on the research of GRA models Purpose – The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models. Design/methodology/approach – Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively. Findings – The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space. Originality/value – The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc. http://www.deepdyve.com/assets/images/DeepDyve-Logo-lg.png Grey Systems Theory and Application Emerald Publishing

A summary on the research of GRA models

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References (37)

Publisher
Emerald Publishing
Copyright
Copyright © 2013 Emerald Group Publishing Limited. All rights reserved.
ISSN
2043-9377
DOI
10.1108/20439371311293651
Publisher site
See Article on Publisher Site

Abstract

Purpose – The purpose of this paper is to review systematically the research of grey relation analysis (GRA) models. Design/methodology/approach – Three different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively. Findings – The GRA models developed from the models based on relation coefficients of each point in the sequences in early days to the generalized GRA models based on integral or overall perspective. It evolved from the GRA models which measure similarity based on nearness, into the models which consider similarity and nearness, respectively. The objects of the research advanced from the analysis of relationship among curves to that among curved surfaces, and further to the analysis of relationship in three‐dimensional space and even the relationship among super surfaces in n‐dimensional space. Originality/value – The further research on GRA models is proposed. One is about the property of GRA model. An in‐depth knowledge about the properties of GRA model will help people to understand its function, applicable area and requirements for modelling. The other one is about the extension of research object system. The object to be analysed should be extended from the common sequence of real numbers to grey numbers, vectors, matrices, and even multi‐dimensional matrices, etc.

Journal

Grey Systems Theory and Application – Emerald Publishing

Published: Jan 25, 2013

Keywords: Grey systems; Research work; Modelling; Grey relation analysis; GRA models; Relation coefficient; Absolute degree of grey relation; n‐dimensional relation space

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