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Aggregation of Epistemic Uncertainty: A New Interpretation of the Certainty Factor with Possibility Theory and Causation Events

Information aggregation has a long history of studies. It has been used in decision-making, sensor fusion, information retrieval, affective intelligence and many other applications for combining certainties, reliabilities, sentiments and other degrees of information to judge something in the real world. The paper dares to revisit a traditional and seemingly forgotten representation of uncertainty called Certainty Factors, and discusses a new interpretation with Possibility theory and causation events. Then it develops a few aggregation functions of uncertainties derived from distinct pieces of evidence. The Certainty Factors had been criticized due to lack of sound mathematical interpretation from the viewpoint of Probability theory. Thus, the paper first tries to establish a theory for a sound interpretation using Possibility theory. Then it examines the aggregation based on the interpretation. It proposes four combination functions with sound theoretical basis, one of which is exactly the same as the combination criticized for long time.