Variance based determination of three-way decisions using probabilistic rough sets

Abstract

The probabilistic rough sets is an important generalization of rough sets where a pair of thresholds is used to form new rough regions. The pair of thresholds controls different quality related criteria such as classification accuracy, precision, uncertainty, costs and risks of rough sets based three-way decision making. In this article, we introduce variance based criteria for determining the thresholds including within region variance, between region variance and ratio of the two variances. In particular, we examine the variance or spread in conditional probabilities of equivalence classes contained in different probabilistic regions. We also show that the determination of thresholds may be considered based on optimization of the proposed criteria.