An optimized fractional grey model based on weighted least squares and its application
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...
| Main Authors: | , |
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| Format: | Article |
| Language: | English |
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AIMS Press
2023-01-01
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| Series: | AIMS Mathematics |
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| Online Access: | https://www.aimspress.com/article/doi/10.3934/math.2023198?viewType=HTML |
| _version_ | 1797950795525652480 |
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| author | Caixia Liu Wanli Xie |
| author_facet | Caixia Liu Wanli Xie |
| author_sort | Caixia Liu |
| collection | DOAJ |
| description | 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. |
| first_indexed | 2024-04-10T22:20:51Z |
| format | Article |
| id | doaj.art-5c467777e01d4e4eb7fa2c37f9bfe4f6 |
| institution | Directory Open Access Journal |
| issn | 2473-6988 |
| language | English |
| last_indexed | 2024-04-10T22:20:51Z |
| publishDate | 2023-01-01 |
| publisher | AIMS Press |
| record_format | Article |
| series | AIMS Mathematics |
| spelling | doaj.art-5c467777e01d4e4eb7fa2c37f9bfe4f62023-01-18T01:14:03ZengAIMS PressAIMS Mathematics2473-69882023-01-01823949396810.3934/math.2023198An optimized fractional grey model based on weighted least squares and its applicationCaixia Liu 0Wanli Xie11. College of Intelligent Education, Jiangsu Normal University, Xuzhou, China 2. Jiangsu Engineering Research Center of Educational Informationization, Jiangsu Normal University, Xuzhou, China3. College of Communication, Qufu Normal University, Rizhao, ChinaThe 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.https://www.aimspress.com/article/doi/10.3934/math.2023198?viewType=HTMLgrey modelfractional-order accumulationweighted least squareswater consumption |
| spellingShingle | Caixia Liu Wanli Xie An optimized fractional grey model based on weighted least squares and its application AIMS Mathematics grey model fractional-order accumulation weighted least squares water consumption |
| title | An optimized fractional grey model based on weighted least squares and its application |
| title_full | An optimized fractional grey model based on weighted least squares and its application |
| title_fullStr | An optimized fractional grey model based on weighted least squares and its application |
| title_full_unstemmed | An optimized fractional grey model based on weighted least squares and its application |
| title_short | An optimized fractional grey model based on weighted least squares and its application |
| title_sort | optimized fractional grey model based on weighted least squares and its application |
| topic | grey model fractional-order accumulation weighted least squares water consumption |
| url | https://www.aimspress.com/article/doi/10.3934/math.2023198?viewType=HTML |
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