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

doi:10.23919/JSEE.2024.000021

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

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.

Figures/Tables 9

Fig 1

Table 1

Fig 2

Fig 3

Table 2

Fig 4

Table 3

Table 4

Table 5

References 42

1	DENG J L The grey control system. Journal of HuaZhong Institute of Technology, 1982, (3): 9- 18.
2	LIU S F. Grey systems theory and its applications. 9th ed. Beijing: Science Press, 2021. (in Chinese)
3	RAJESH R A novel advanced grey incidence analysis for investigating the level of resilience in supply chains. Annals of Operations Research, 2022, 308 (1/2): 441- 490. doi: 10.1007/s10479-020-03641-5
4	NAEEM M S, AHMAD N, JAVED Z, et al Multi-response optimization for the development of an activated carbon web as interlining for higher electrical conductivity and EMI shielding using grey relational analysis. Fibres & Textiles in Eastern Europe, 2021, 29 (1): 57- 65.
5	FU Y F, YANG R N, LIU X D, et al Software effort estimation method based on grey relational analysis. Systems Engineering and Electronics, 2012, 34 (11): 2384- 2389.
6	HSU C J, HUANG C Y Comparison of weighted grey relational analysis for software effort estimation. Software Quality Journal, 2011, 19 (1): 165- 200. doi: 10.1007/s11219-010-9110-y
7	ZHANG J T, LI S S, WANG X K Method of radar anti-jamming performance evaluation based on grey correlation-fuzzy comprehensive evaluation. Systems Engineering and Electronics, 2021, 43 (6): 1557- 1563.
8	DANG Y G, LIU S F, LIU B, et al Improvement on degree of grey slope incidence. Engineering Science, 2004, 6 (3): 41- 44.
9	LIU Y, LIU S F, JEFFREY F A new absolute degree of grey incidence model and application. Chinese Journal of Management Science, 2012, 20 (5): 173- 177.
10	TANG W X The concept and the computation method of T’s correlation degree. Journal of Applied Statistics and Management, 1995, 14 (1): 34- 37.
11	FENG H L, CHEN Y M, YANG M Discussion on the positive and negative of T’s correlation degree. Statistics & Decision, 2012, 28 (19): 15- 17.
12	WANG Q Y, ZHAO X H The relational analysis of C-mode. Journal of Huazhong University of Science and Technology, 1999, 27 (3): 76- 78.
13	WU L F, WANG Y N, LIU S F Grey convex relation and its properties. System Engineering-Theory & Practice, 2012, 32 (7): 1501- 1505.
14	PAN P G, CHEN Y M, XIE H Y Study on grey H-convex relational degree model. Statistics & Decision, 2016, 453 (9): 31- 34.
15	LIU X M, KE L, YU J J A improved model to the absolute degree of grey incidence. Mathematics in Practice and Theory, 2018, 48 (10): 16- 22.
16	JIANG S Q, LIU S F, LIU Z X, et al Grey incidence decision making model based on area. Control and Decision, 2015, 30 (4): 685- 690.
17	ZHANG Q S, GUO X J Grey relation entropy method of grey relation analysis. System Engineering-Theory & Practice, 1996, 16 (8): 8- 12.
18	SHI Y M Improvement and application of grey correlation analysis. Journal of Highway Transportation University, 1994, 14 (3): 94- 100.
19	ZHAO Y L, WEI S Y, MEI Z X Grey euclid relation grade. Journal of Guangxi University, 1998, 23 (1): 10- 13.
20	ZHANG Q S, DENG J L, SHAO Y A grey correlational analysis by the method of degree of balance and approach. Journal of Huazhong University of Science and Technology, 1995, 23 (11): 94- 98.
21	LIU W F, HE X A new grey relational degree model. Statistics & Decision, 2011, 27 (14): 160- 161.
22	PEI L L, WANG Z X, SHEN C G Study on grey distance correlation degree model and its properties. Statistics & Decision, 2010, 26 (16): 11- 13.
23	ZHANG L, CHANG T Q, WANG Q S, et al An improvement method of grey incidence degree mode. Fire Control & Command Control, 2012, 37 (1): 121- 124.
24	LIU S F, XIE N M, FORREST J On new models of grey incidence analysis based on visual angle of similarity and nearness. Systems Engineering-Theory & Practice, 2010, 30 (5): 881- 887.
25	HUANG G Q, SU L Analysis of effectiveness evaluation based on improved gray synthesize relational degree. Fire Control & Command Control, 2015, 37 (3): 90- 93.
26	ZHANG K, LIU S F Extended clusters of grey incidence for panel data and its application. System Engineering-Theory & Practice, 2010, 30 (7): 1253- 1259.
27	LIU Y , DU J L, LI J. A novel grey object matrix incidence clustering model for panel data and its application. Scientia Iranica, 2021, 28(1): 371−385.
28	LIU Z, DANG Y G, QIAN W Y, er al Grey grid incidence model based on panel data. System Engineering-Theory & Practice, 2014, 34 (4): 991- 996.
29	SUN J, DANG Y G, ZHU X Y, et al A grey spatiotemporal incidence model with application to factors causing air pollution. Science of the Total Environment, 2020, 759 (12): 143576.
30	LUO D, ZHANG M M The grey incidence model of B-mode based on panel data and its application. Control and Decision, 2020, 35 (6): 1476- 1482.
31	WU L F, LIU S F, YAO L G, et al Grey convex relational degree and its application to evaluate regional economic sustainability. Scientia Iranica, 2013, 20 (1): 44- 49.
32	WU H H, QU Z F The grey curvature incidence model based on panel data. Control and Decision, 2020, 35 (5): 1072- 1076.
33	WU H H, QU Z F Gray clustering model based on the degree of dynamic weighted incidence for panel data and its application. Grey Systems: Theory and Application, 2020, 10 (4): 413- 423. doi: 10.1108/GS-09-2019-0040
34	WANG J J, HIPEL K W, DANG Y G. An improved grey dynamic trend incidence model with application to factors causing smog weather. Expert Systems with Applications, 2017, 87: 240−251.
35	ZHANG K, CUI L, YIN Y A multivariate grey incidence model for different scale data based on spatial pyramid pooling. Journal of Systems Engineering and Electronics, 2020, 31 (4): 770- 779. doi: 10.23919/JSEE.2020.000052
36	WU H H, LIU S F, FANG Z G Grey tetrahedral grid incidence analysis model based on panel data and its application. Control and Decision, 2022, 37 (11): 3033- 3041.
37	GUO Y F, FENG Z G Calculation of variation of discrete surface. Journal of Henan University of Science and Technology: Natural Science, 2015, 36 (2): 88- 91.
38	MI Y F, SUN K, LI L, et al Spatiotemporal pattern analysis of PM2. 5 and the driving factors in the middle Yellow River urban agglomerations. Journal of Cleaner Production, 2021, 299, 126904.
39	YANG Y H, TANG D L, YANG X Investigating the spatiotemporal variations of the impact of urbanization on haze pollution using multiple indicators. Stochastic Environmental Research and Risk Assessment, 2020, 35 (3): 703- 717.
40	GAN T, YANG H C, LIANG W How do urban haze pollution and economic development affect each other? Empirical evidence from 287 Chinese cities during 2000−2016. Sustainable Cities and Society, 2021, 65, 102642. doi: 10.1016/j.scs.2020.102642
41	SONG C Z, YIN G W, LU Z L, et al Industrial ecological efficiency of cities in the Yellow River Basin in the background of China’s economic transformation: spatial-temporal characteristics and influencing factors. Environmental Science and Pollution Research, 2022, 29 (3): 4334- 4349. doi: 10.1007/s11356-021-15964-2
42	LYU W N, LI Y, GUAN D B, et al Driving forces of Chinese primary air pollution emissions: an index decomposition analysis. Journal of Cleaner Production, 2016, 133, 136- 144. doi: 10.1016/j.jclepro.2016.04.093

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