An optimized fractional grey model based on weighted least squares and its application
An optimized fractional grey model based on weighted least squares and its application
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DOI：
10.3934/math.2023198
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发表时间：
2022-01-01
期刊：
影响因子：
2.2
通讯作者：
Xie, Wanli
中科院分区：
文献类型：
--
作者：
Liu, Caixia;Xie, Wanli
分数灰色模型是对小数据样本进行建模的有效工具。由于其数学建模的本质特征，它引起了学者们的极大兴趣。为了提高模型的准确性并扩大模型的应用范围，许多学者提出了许多引人注目的方法。例子包括初始值优化、阶次优化等。本文采用加权最小二乘法来提高模型的准确性。本研究的第一步是开发一种基于加权最小二乘算子的新型分数预测模型。此后，确定所提出模型的累积阶数，并评估优化算法的稳定性。最后通过三个实际案例验证了模型的有效性，并进一步探讨了模型的误差方差。根据结果，所提出的模型比比较模型更准确，并且可以应用于实际情况。
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.