Grey prediction models have been widely used in various fields of society due to their high prediction accuracy; accordingly, there exists a vast majority of grey models for equidistant sequences; however, limited research is focusing on nonequidistant sequence. The development of nonequidistant grey prediction models is very slow due to their complex modeling mechanism. In order to further expand the grey system theory, a new nonequidistant grey prediction model is established in this paper. To further improve the prediction accuracy of the NEGM (1, 1, t²) model, the background values of the improved nonequidistant grey model are optimized based on Simpson formula, which is abbreviated as INEGM (1, 1, t²). Meanwhile, to verify the validity of the proposed model, this model is applied in two real-world cases in comparison with three other benchmark models, and the modeling results are evaluated through several commonly used indicators. The results of two cases show that the INEGM (1, 1, t²) model has the best prediction performance among these competitive models.

中文翻译：

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基于Simpson公式的改进非等距灰色模型及其应用。

灰色预测模型具有较高的预测精度，因此已广泛应用于社会的各个领域。因此，对于等距序列，存在大量的灰色模型。然而，有限的研究集中在非等距序列上。非等距灰色预测模型的开发由于其复杂的建模机制而非常缓慢。为了进一步扩展灰色系统理论，本文建立了新的非等距灰色预测模型。为了进一步改善NEGM的预测精度（1，1，吨²）模型，该改进的nonequidistant灰色模型的背景值被优化基于辛普森式，其被缩写为INEGM（1，1，吨²）。同时，为验证所提出模型的有效性，将该模型与其他三个基准模型进行了比较，将其应用于两个实际案例中，并通过几种常用指标对建模结果进行了评估。两种情况的结果表明，在这些竞争模型中，INEGM（1，1，t ²）模型具有最佳的预测性能。