考虑因素耦合关系的新型灰色关系分析模型的构建与应用

IF 3.2 3区工程技术 Q1 MATHEMATICS, INTERDISCIPLINARY APPLICATIONS Grey Systems-Theory and Application Pub Date : 2024-09-10 DOI:10.1108/gs-04-2024-0046

Aqin Hu, Naiming Xie

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引用次数: 0

摘要

目的本文旨在探索一种新的灰色关系分析模型，以衡量水环境状况评价指标之间的耦合关系。设计/方法/途径首先给出样本矩阵的二元指数子矩阵，然后利用矩阵与自身转置的乘积来衡量指标之间的耦合关系。首先给出样本矩阵的二元指数子矩阵，然后利用矩阵与自身转置的乘积来衡量指数的特征和指标间的耦合关系。第三，根据矩阵规范定义灰色关系系数，并提出灰色耦合关系分析模型。研究了其特性、归一化、对称性、对乘法的关系阶不变性。本文还表明，该模型在长江沿岸八个城市的水环境状况评估中表现非常出色。

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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.