This work uses the vector-valued Bernoulli equation to build a nonlinear multi-variable grey Bernoulli model, which is available to describe the nonlinear relationship between the output variables. By using approximation, the proposed model can be implemented with high time efficiency. Additionally, the Sine Cosine Algorithm is employed to determine the Bernoulli exponent, thereby enhancing prediction accuracy. To evaluate the predictive performance of the proposed model, three case studies using three real-world data sets with different features of predicting per capita household income, fuel prices and crude oil prices are carried out. The results are compared with three existing grey multi-input multi-output models. Experimental results demonstrate that the proposed model excels in handling nonlinear relationships between variables and has strong robustness against noise, consistently delivering lower error values, demonstrating superior predictive performance.

中文翻译：

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非线性多变量灰色伯努利模型及其应用


本文利用向量值伯努利方程建立非线性多变量灰色伯努利模型，可以描述输出变量之间的非线性关系。通过使用近似，所提出的模型可以以高时间效率实现。另外，采用正弦余弦算法确定伯努利指数，从而提高预测精度。为了评估所提出模型的预测性能，使用三个现实世界数据集进行了三个案例研究，这些数据集具有预测人均家庭收入、燃料价格和原油价格的不同特征。结果与现有的三种灰色多输入多输出模型进行了比较。实验结果表明，所提出的模型擅长处理变量之间的非线性关系，并且对噪声具有很强的鲁棒性，始终提供较低的误差值，表现出卓越的预测性能。