Probabilistic rough sets

As quantitative generalizations of Pawlak rough sets, probabilistic rough sets consider degrees of overlap between equivalence classes and the set. An equivalence class is put into the lower approximation if the conditional probability of the set, given the equivalence class, is equal to or above one threshold; an equivalence class is put into the upper approximation if the conditional probability is above another threshold hold. We review a basic model of probabilistic rough sets (i. e., decision-theoretic rough set model) and variations. We present the main results of probabilistic rough sets by focusing on three issues (a) interpretation and calculation of the required thresholds, (b) estimation of the required conditional probabilities, and (c) interpretation and applications of probabilistic rough set approximations.