A summary on the research of GRA models

Abstract

PurposeThe purpose of this paper is to review systematically the research of grey relation analysis (GRA) models.Design/methodology/approachThree different approaches, the springboard to build a GRA model, the angle of view in modelling, and the dimension of objects, are analysed, respectively.FindingsThe 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/valueThe 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.

Assessment of the track condition using the Gray Relational Analysis method

“…Theory of gray systems was proposed by prof. J-L. Deng, and has many different research areas and uses [4]. One of them is the study of similarity between data sequences (GRAs) [10]. Studying the similarity of data in different collections is of great importance in this methodology as it allows for a comparison of a given drive profile with the reference for a good track condition.…”

“…An example is a generalized GRA model, which is used to analyze relationships between sequences and measures based on distance and similarity. A detailed overview of the methods can be found in [10]. Certain other measures have been proposed in [13].…”

Grey social media engagement analysis

“…Moreover, it can easily switch between a quantitative, a qualitative or a mixed analysis. The obtained values for GRA are between 0 and 1 and they are underlying a stronger relationship among the considered values when the calculated GRA approaches 1 (Sifeng Liu et al, 2013). The evolution of the usage of the grey relational analysis over the time in different economic and social areas has been drawn recently, emphasising more its application into the practical cases encountered in economics and social sciences (Orzan et al, 2015).…”

The interaction between the innovation and the output of China'S High-tech industries based on grey relational analysis

“…Relative GRA model of Equation (4) uses initializing transformation of the sequences to establish an absolute GRA model, and mainly deals with the relation of changing velocity of sequences. And Equation (5) is a synthetic GRA model by combining of the absolute degree of grey incidences and relative degree of incidences, where synthetic coefficient θ could be determined according to the relative importance of the two [13] . Although the above data span a long period of time, the statistical caliber of R&D investment changed from funding for scientific and technological activities to R&D expenditures in 2008.…”