An optimized fractional grey model based on weighted least squares and its application

Caixia Liu; Wanli Xie; Caixia Liu; Wanli Xie

doi:10.3934/math.2023198

AIMS Mathematics

2023, Volume 8, Issue 2: 3949-3968. doi: 10.3934/math.2023198

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Research article

An optimized fractional grey model based on weighted least squares and its application

Caixia Liu ^1,2,
Wanli Xie ^{3
,
,}

1.
College of Intelligent Education, Jiangsu Normal University, Xuzhou, China
2.
Jiangsu Engineering Research Center of Educational Informationization, Jiangsu Normal University, Xuzhou, China
3.
College of Communication, Qufu Normal University, Rizhao, China

Received: 27 September 2022 Revised: 10 November 2022 Accepted: 17 November 2022 Published: 30 November 2022
MSC : 62-XX, 65-XX

The fractional grey model is an effective tool for modeling small samples of data. Due to its essential characteristics of mathematical modeling, it has attracted considerable interest from scholars. A number of compelling methods have been proposed by many scholars in order to improve the accuracy and extend the scope of the application of the model. Examples include initial value optimization, order optimization, etc. The weighted least squares approach is used in this paper in order to enhance the model's accuracy. The first step in this study is to develop a novel fractional prediction model based on weighted least squares operators. Thereafter, the accumulative order of the proposed model is determined, and the stability of the optimization algorithm is assessed. Lastly, three actual cases are presented to verify the validity of the model, and the error variance of the model is further explored. Based on the results, the proposed model is more accurate than the comparison models, and it can be applied to real-world situations.
- grey model,
- fractional-order accumulation,
- weighted least squares,
- water consumption
Citation: Caixia Liu, Wanli Xie. An optimized fractional grey model based on weighted least squares and its application[J]. AIMS Mathematics, 2023, 8(2): 3949-3968. doi: 10.3934/math.2023198

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Abstract

The fractional grey model is an effective tool for modeling small samples of data. Due to its essential characteristics of mathematical modeling, it has attracted considerable interest from scholars. A number of compelling methods have been proposed by many scholars in order to improve the accuracy and extend the scope of the application of the model. Examples include initial value optimization, order optimization, etc. The weighted least squares approach is used in this paper in order to enhance the model's accuracy. The first step in this study is to develop a novel fractional prediction model based on weighted least squares operators. Thereafter, the accumulative order of the proposed model is determined, and the stability of the optimization algorithm is assessed. Lastly, three actual cases are presented to verify the validity of the model, and the error variance of the model is further explored. Based on the results, the proposed model is more accurate than the comparison models, and it can be applied to real-world situations.

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