Combining uncertain information of differing modalities

In this paper we consider approaches for combining separately possibilistic uncertainty, probabilistic uncertainty and situations where both forms of uncertainty appear. An approach to probability aggregation using rational consensus with equi-weighting is developed. This aggregation is analyzed with information measures as one way to assess combinations and understand the impact on uncertainty. The analysis is based on combinations of bounding cases of probability distributions. Measures of conflict and the effect on information are developed. Next possibility transformations are used and illustrated by three representative possibility cases. The resultant transformed probabilities are aggregated with general probability distributions and the result evaluated with information measures as before. Finally a general approach to combining possibility distributions directly using quality criteria is described. An example is provided to illustrate the basic possibility distribution aggregation fusion developed.