Novel grey variation relational analysis model for panel data and its application

doi:10.23919/JSEE.2024.000021

Journal of Systems Engineering and Electronics ›› 2025, Vol. 36 ›› Issue (2): 483-493.doi: 10.23919/JSEE.2024.000021

• • 上一篇

收稿日期:2023-03-13 出版日期:2025-04-18 发布日期:2025-05-20

Novel grey variation relational analysis model for panel data and its application

Honghua WU¹^,²^,*(), Zhongfeng QU¹()

¹ School of Mathematical Sciences, University of Jinan, Jinan 250022, China
² College of Economics and Management, Nanjing University of Aeronautics and Astronautics, Nanjing 211106, China

Received:2023-03-13 Online:2025-04-18 Published:2025-05-20
Contact: Honghua WU E-mail:ss_wuhh@ujn.edu.cn;ss_quzf@ujn.edu.cn
About author:
WU Honghua was born in 1978. He received his M.S. degree from Beijing Institute of Technology in 2005. He is currently pursuing his Ph.D. degree in management science and engineering from Nanjing University of Aeronautics and Astronautics, Nanjing, China. He is currently an associate professor of the School of Mathematical Sciences, University of Jinan. His research interests include the grey system theory and applications. E-mail: ss_wuhh@ujn.edu.cn

QU Zhongfeng was born in 1979. He received his M.S. degree from Harbin Institute of Technology in 2005. He is currently an associate professor of the School of Mathematical Sciences, University of Jinan. His research interests include applied mathematics and statistical analysis. E-mail: ss_quzf@ujn.edu.cn
Supported by:
This work was supported by the National Natural Science Foundation of China (72271124;72071111), Shandong Natural Science Foundation (ZR2023MG070) and the Social Science Planning Project of Shandong Province (23CGLJ03;21CTJJ01).

摘要/Abstract

Abstract:

Based on the variation of discrete surface, a new grey relational analysis model, called the grey variation relational analysis (GVRA) model, is proposed in this paper. Meanwhile, the proposed model avoids the inconsistent results caused by different construction of discrete surface of panel data or the change in the order of indicators or objects in existing grey relational analysis models. Firstly, the submatrix of the sample matrix is given according to the permutation and combination theory. Secondly, the amplitude of the submatrix is calculated and the variation of discrete surface is obtained. Then, a grey relational coefficient is presented by variation difference, and the GVRA model is established. Furthermore, the properties of the proposed model, such as normality, symmetry, reflexivity, translation invariant, and number multiplication invariant, are also verified. Finally, the proposed model is used to identify the driving factors of haze in the cities along the Yellow River in Shandong Province, China. The result reveals that the proposed model can effectively measure the relationship between panel data.

Key words: grey relational analysis, grey system theory, variation, discrete surface

. [J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 483-493.

Honghua WU, Zhongfeng QU. Novel grey variation relational analysis model for panel data and its application[J]. Journal of Systems Engineering and Electronics, 2025, 36(2): 483-493.

图/表 9

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City	Indicator	2014	2015	2016	2017	2018	2019	2020
JN	PM_2.5	88.58	89.75	75.33	63.58	50.92	54.92	50.08
JN	PM₁₀	172.42	161.83	146.08	125.92	102.25	108.75	91.92
DY	PM_2.5	77.42	79.25	64.17	56.42	45.25	48.67	45.67
DY	PM₁₀	147.42	135.58	120.33	107.67	90.83	92.67	80.50
LC	PM_2.5	98.33	98.33	85.75	69.75	56.83	58.83	53.33
LC	PM₁₀	171.17	160.00	149.00	130.42	108.50	111.50	93.42
BZ	PM_2.5	84.92	78.92	74.00	66.00	52.83	53.33	48.83
BZ	PM₁₀	134.50	125.00	126.00	101.17	86.50	88.17	77.42
HZ	PM_2.5	99.67	94.17	81.33	68.92	55.58	59.58	53.33
HZ	PM₁₀	160.50	154.42	141.83	129.92	112.00	115.92	105.75
ZB	PM_2.5	94.50	87.33	75.00	64.67	52.17	58.25	54.50
ZB	PM₁₀	167.17	160.25	133.50	118.25	96.33	106.75	92.58
JNing	PM_2.5	88.25	80.83	69.58	54.83	47.08	56.83	53.42
JNing	PM₁₀	154.83	140.08	115.50	104.33	94.75	95.92	81.17
TA	PM_2.5	76.25	69.08	65.75	57.25	48.42	57.33	50.92
TA	PM₁₀	131.42	127.08	115.67	95.67	93.08	106.58	93.50
DZ	PM_2.5	104.67	100.33	82.00	67.17	52.17	53.58	49.25
DZ	PM₁₀	153.50	164.25	151.67	119.92	102.00	104.08	92.83

Indicator	Y₁	Y₂	Y₃	Y₄	Y₅	Y₆	Y₇	Y₈	Y₉	Y₁₀	Y₁₁	Y₁₂	Y₁₃	Y₁₄	Y₁₅	Y₁₆	Y₁₇
PM_2.5	0.962	0.920	0.948	0.932	0.916	0.879	0.905	0.902	0.938	0.851	0.865	0.806	827	0.916	0.946	0.817	0.949
PM₁₀	0.937	0.890	0.916	0.901	0.886	0.852	0.935	0.873	0.944	0.826	0.839	0.782	0.803	0.886	0.914	0.794	0.980

Indicator	Driver
PM_2.5	GDP, VSI, VTI, UIS, VAI, UR, IERD, EERD, CGA, DI, ECR
PM₁₀	GDP, VTI, UIS, UR, EERD, DI, ECR

Model	Normality	Symmetry	Reflexivity	Translation invariant	Number multiplication invariant	Uniqueness of the result
EGRA	√	√	√	√	√	×
GCRA	√	√	√	√	√	×
EGBRA	√	√	√	√	√	×
GVRA	√	√	√	√	√	√

Model	Y₁	Y₂	Y₃	Y₄	Y₅	Y₆	Y₇	Y₈	Y₉	Y₁₀	Y₁₁	Y₁₂	Y₁₃	Y₁₄	Y₁₅	Y₁₆	Y₁₇
EGRA	0.513	0.538	0.511	0.513	0.551	0.536	0.560	0.512	0.520	0.542	0.559	0.534	0.509	0.515	0.521	0.537	0.536
GCRA	0.567	0.669	0.512	0.673	0.648	0.568	0.705	0.527	0.446	0.561	0.516	0.565	0.565	0.543	0.776	0.499	0.801
EGBRA	0.603	0.641	0.530	0.710	0.631	0.567	0.742	0.556	0.446	0.559	0.538	0.492	0.508	0.539	0.772	0.418	0.814

Novel grey variation relational analysis model for panel data and its application

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