Combining rough sets and Bayes' rule

In rough set theory with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors a re closely related with the lower and the upper approximation of a set, bas ic notions of rough set theory. It is shown that these two factors satisfy the Bayes' rule. The Bayes' rule in our case simply shows some relationship in the data, wit hout referring to prior and posterior probabilities intrinsically associate d with Bayesian inference. This relationship can be used to "invert" decisi on rules, i.e., to find reasons (explanation) for decisions thus providing inductive as well as deductive inference in our scheme.