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的数学算子，记为$\cupplus$，用于信息聚合。该算子旨在通过直接融合概率分布来增强传统方法，它促进了概率密度的组合，为概率分析提供了一种细致入微的途径。我们将此算子应用于一个个性化激励场景，以说明其在实际背景中的潜力。本文的主要贡献在于引入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向前迈进了一步。