# JAMC

Article http://dx.doi.org/10.26855/jamc.2023.12.009

# A New Grey Prediction IANGM (1,1, k, k2) Model

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Xinyi Dong

School of Mathematics and Information, China West Normal University, Nanchong, Sichuan, China.

*Corresponding author: Xinyi Dong

Published: January 24,2024

## Abstract

In this paper, a new grey prediction IANGM (1,1, k, k2) model with quadratic time-varying function is constructed, which is suitable for approximate homogeneous exponential type, approximate non-homogeneous exponential type, exponential linear combination type, and exponential parabolic combination type characteristic sequence. The undetermined coefficient method is used to determine the shadow equation matching the model, and the time response formula of the IANGM (1,1, kk2) model is derived based on the constant variation method. Through numerical simulation and double modeling analysis of China's domestic heat consumption and soft soil foundation settlement data from 2011 to 2020, the results show that the IANGM (1,1, kk2) model has higher simulation and prediction accuracy.

## References

[1] Liu S F, Dang Y G, & Fang Z G. Grey system theory and application [M]. Beijing: Science Press, 2018.

[2] Long Z, Wei Y, & Long X. A new method of background value optimization in grey prediction model [J]. Journal of Grey System, 2015, 18(01): 41-46.

[3] Xiang X W, Zhang P, & Yu L. Forecasting oil consumption with novel fractional grey prediction model based on Simpson formula [J]. Asia J Math, 2019, 15(02): 1-27.

[4] Cheng ML, Shi G J, & Xiang M Y. On the improvement of the parameter estimation of the grey model GM(1,1) and model application [J]. Communications in Statistics-Simulation and Computation, 2020, 49(05): 1367-1384.

[5] Dai Y Q, Yan Y L, & Liu Z. Prediction and analysis of the total health expenditure and its composition trend in Beijing based on GM (1,1) model [J]. Modern Preventive Medicine, 2021, 48(11): 1996-2000.

[6] Tang L W & Lu Y Y. An Improved Non-equal Interval GM(1,1) Model Based on Grey Derivative and Accumulation [J]. Journal of Grey System, 2020, 32(02): 77-88.

[7] Wu Z T & Zhang T. The improvement and application of the GM(1,1) model [J]. Statistics And Decision, 2019, 35(09): 15-18.

[8] Yin K D, Geng Y, & Li X M. Improved grey prediction model based on exponential grey action quantity [J]. Journal of Systems Engineering and Electronics, 2018, 29(03): 560-570.

[9] Xu J L & Chen Y J. DGM(2,1) model based on grey action and grey derivative optimization [J]. Journal of Luoyang Normal University, 2023, 42(05): 1-8.

[10] Zhang Y. Optimize the MGM(1,m) model of grey derivative [J]. The Practice And Understanding of Mathematics, 2022, 52(10): 136-141.

[11] Cui J, Dang Y G, & Liu S F. A new grey prediction model and its modeling mechanism [J]. Control and Decision, 2009, 24(11): 1702-1706.

[12] Cui X K & Lu X Y. Prediction method of agricultural product yield based on NGM(1,1,k) model [J]. Microelectronics & Computer, 2011, 28(08): 201-203+207.

[13] Kong X H, Chen J J, & Zhao Y. Optimization of background value and time response function of grey GM(1,1,k,k^2 ) model [J]. Operations Research, and Management Science, 2022, 31(07): 109-113.

[14] Liu J F, Liu S F, & Fang Z G. Fractional-order Reverse Accumulation Generation GM(1,1) Model and its Applications [J]. Journal of Grey System, 2015, 27(4): 52-62.

[15] Zhang K, Wang C Y, & He L J. An improved GOM(1,1) model and its application [J]. Journal of Engineering Mathematics, 2021, 38(01): 38-48.

[16] Zeng L & Jiang A P. Four basic forms of reverse accumulation GOM(1,1) model and their comparison [J]. Practice and Cognition of Mathematics, 2020, 50(06): 219-228.

[17] Ding S, Dang Y G, & Xu N. Construction and optimization of NGOM(1,1) model with approximate non-homogeneous exponential decreasing sequence [J]. Control and Decision, 2017, 32(08): 1457-1464.

[18] Yang Z, Ren P, & Dang Y G. Reverse cumulative generation and optimization of grey GOM(1,1) model [J]. Theory and Practice of Systems Engineering, 2009, 29(08): 160-164.

[19] Lian J W, Dang Y G, & Wang Z X. The characteristics of reverse accumulation generation and the optimization of GOM(1,1) model [J]. Theory and Practice of Systems Engineering, 2013, 33(09): 2306-2312.

[20] Wang J. Optimization and application of a new grey prediction model [J]. Statistics and Decision, 2015(17): 86-88.

[21] Chen J. & Chen Y J. Construction of IANGM(1,1,k) model for approximate non-homogeneous exponential increasing sequence [J]. Statistics and Decision, 2020, 36(20): 24-27.

[22] Xu H F, Liu S F, & Fang Z G. Optimization of grey action of GM(1,1) model [J]. Practice and Cognition of Mathematics, 2010, 40(02): 26-32.

[23] National Bureau of Statistics of China. China statistical yearbook [M]. Beijing: China Statistical Publishing House, 2022.

[24] Niu X X. Analysis and improvement of GM (2,1) model for settlement prediction of soft soil foundation [J]. Safety and Environmental Engineering, 2014, 21(02): 139-142.

## How to cite this paper

A New Grey Prediction IANGM (1,1, k, k2) Model

How to cite this paper: Xinyi Dong. (2023) A New Grey Prediction IANGM  (1,1, kk2) ModelJournal of Applied Mathematics and Computation7(4), 490-499.

DOI: http://dx.doi.org/10.26855/jamc.2023.12.009