Rough sets and Bayes factor

We present a novel approach to understanding the concepts of the theory of rough sets in terms of the inverse probabilities derivable from data. It is related to the Bayes factor known from the Bayesian hypothesis testing methods. The proposed Rough Bayesian model (RB) does not require information about the prior and posterior probabilities in case they are not provided in a confirmable way. We discuss RB with respect to its correspondence to the original Rough Set model (RS) introduced by Pawlak and Variable Precision Rough Set model (VPRS) introduced by Ziarko. We pay a special attention on RB's capability to deal with multi-decision problems. We also propose a method for distributed data storage relevant to computational needs of our approach.