An Application of Bayesian Confirmation Theory for Three-Way Decision.

Bayesian confirmation theory studies how a piece of evidence confirms a hypothesis. In a qualitative approach, a piece of evidence may confirm, disconfirm, or be neutral with respect to a hypothesis. A quantitative approach uses Bayesian confirmation measures to evaluate the degree to which a piece of evidence confirms a hypothesis. In both approaches, we may perform a three-way classification of a set of pieces of evidence for a given hypothesis. The set of evidence is divided into three regions of positive evidence that confirms the hypothesis, negative evidence that disconfirms the hypothesis, and neutral evidence that neither confirms nor disconfirms the hypothesis. In this paper, we investigate three-way classification models in both qualitative and quantitative Bayesian confirmation approaches and explore their relationships to three-way classification models in rough set theory.