This study explores a new mathematical operator, symbolized as $\cupplus$, for information aggregation, aimed at enhancing traditional methods by directly amalgamating probability distributions. This operator facilitates the combination of probability densities, contributing a nuanced approach to probabilistic analysis. We apply this operator to a personalized incentive scenario, illustrating its potential in a practical context. The paper's primary contribution lies in introducing this operator and elucidating its elegant mathematical properties. This exploratory work marks a step forward in the field of information fusion and probabilistic reasoning.

翻译：本研究探讨了一种新型数学算子（以符号$\cupplus$表示），用于信息聚合领域。该算子通过直接融合概率分布来改进传统方法，能够实现概率密度的组合，为概率分析提供了精细化的研究路径。我们将该算子应用于个性化激励场景，验证了其在实际情境中的潜力。本文的核心贡献在于提出该算子并阐明其优美的数学性质，这项探索性工作标志着信息融合与概率推理领域迈出了新的一步。