Thresholds determination for probabilistic rough sets with genetic algorithms

Abstract

Probabilistic rough sets define the lower and upper approximations and the corresponding three regions by using a pair of (α, β) thresholds. Many attempts have been made to determine or calculate effective (α, β) threshold values. A common principle in these approaches is to combine and utilize some intelligent technique with a repetitive process in order to optimize different properties of rough set based classification. In this article, we investigate an approach based on genetic algorithms that repeatedly modifies the thresholds while reducing the overall uncertainty of the rough set regions. A demonstrative example suggests that the proposed approach determines useful threshold values within a few iterations. It is also argued that the proposed approach provide similar results to that of some existing approaches such as the game-theoretic rough sets.