The prediction of the tertiary industry's output value is essential for enhancing the market economic system and providing guidance for the government in formulating relevant economic policies. The tertiary industry encompasses various sectors such as finance and transportation, and its total output value exhibits uncertain and nonlinear trends. Triangular fuzzy number sequences contain more comprehensive information than exact number sequences. Therefore, a nonlinear grey Bernoulli model with conformable fractional accumulation for triangular fuzzy sequences is proposed. Firstly, the conformable fractional accumulation generating operation is utilized to mitigate the volatility tendency of the original sequences. Additionally, a time power function term is introduced to capture the power exponential trend. Furthermore, an improved whale optimization algorithm incorporating opposition-based learning strategy and adaptive control parameters is employed to optimize the model parameters, which has been verified through algorithm comparison experiments. Three existing grey models are used as competing models to validate the prediction accuracy of our proposed model. Finally, we utilize this proposed model to predict the tertiary industry's output values in both Yangtze and Pearl River Deltas for 2024–2026.

中文翻译：

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第三产业总产值预测的三角模糊序列一致分数累加灰色非线性模型


第三产业产值预测对于完善市场经济体制、指导政府制定相关经济政策具有重要意义。第三产业涵盖金融、交通运输等多个行业，其总产值呈现出不确定性、非线性的趋势。三角模糊数列比精确数列包含更全面的信息。因此，提出了三角模糊序列的一致分数累加非线性灰色伯努利模型。首先，利用一致分数累加生成操作来减轻原始序列的波动性倾向。此外，还引入了时间幂函数项来捕获幂指数趋势。此外，采用基于对立学习策略和自适应控制参数的改进鲸鱼优化算法来优化模型参数，并通过算法对比实验得到验证。使用三个现有的灰色模型作为竞争模型来验证我们提出的模型的预测准确性。最后，我们利用该模型预测了2024-2026年长三角和珠三角的第三产业产值。