Decision rules, Bayes' rule and rough sets

This paper concerns a relationship between Bayes' inference rule and decision rules from the rough set perspective. In statistical inference based on the Bayes' rule it is assumed that some prior knowledge (prior probability) about some parameters without knowledge about the data is given first. Next the posterior probability is computed by employing the available data. The posterior probability is then used to verify the prior probability. In the rough set philosophy with every decision rule two conditional probabilities, called certainty and coverage factors, are associated. These two factors are closely related with the lower and the upper approximation of a set, basic notions of rough set theory. Besides, it is revealed that these two factors satisfy the Bayes' rule. That means that we can use to data analysis the Bayes' rule of inference without referring to Bayesian philosophy of prior and posterior probabilities.