  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.
