Aggregation of Epistemic Uncertainty in Forms of Possibility and Certainty Factors

Abstract

Uncertainty aggregation is an important reasoning for making decisions in the real world, which is full of uncertainty. The paper proposes an information source model for aggregating epistemic uncertainties about truth and discusses uncertainty aggregation in the form of possibility distributions. A new combination rule of possibilities for truth is proposed. Then, this paper proceeds to discussion about a traditional but seemingly forgotten representation of uncertainty (i.e., certainty factors (CFs)) and proposes a new interpretation based on possibility theory. CFs have been criticized because of their lack of sound mathematical interpretation from the viewpoint of probability. Thus, this paper first establishes a theory for a sound interpretation using possibility theory. Then it examines aggregation of CFs based on the interpretation and some combination rules of possibility distributions. The paper proposes several combination rules for CFs having sound theoretical basis, one of which is exactly the same as the oft-criticized combination.