Construction and application of a novel grey relational analysis model considering factor coupling relationship

Purpose The purpose of this paper is to explore a new grey relational analysis model to measure the coupling relationship between the indicators for the water environment status assessment. Meanwhile, the model deals with the problem that the changing of indicator order may result in the changing of the degree of grey relation. Design/methodology/approach The binary index submatrix of the sample matrix is given first. Then the product of the matrix and its own transpose is used to measure the characteristics of the index and the coupling relationship between the indicators. Thirdly, the grey relational coefficient is defined based on the matrix norm, and a grey coupling relational analysis model is proposed. Findings The paper provides a novel grey relational analysis model based on the norm of matrix. The properties, normalization, symmetry, relational order invariance to the multiplicative, are studied. The paper also shows that the model performs very well on the water environment status assessment in the eight cities along the Yangtze River. Originality/value The model in this paper has supplemented and improved the grey relational analysis theory for panel data.