Variable Precision Tolerance Rough Set Model

Classical rough set theory provides a new tool to deal with vagueness, uncertainty andincompleteness. The main idea is that using a pair of approximation operators to approximatea given concept.Over the years, generalization of rough set model is one of the most important studycontent. Among them, the the Ziarko variable precision rough set model and tolerance roughset model is two extensions of the classical Pawlak rough set theory,and the differences is asfollow: By setting the threshold parameter (0≤β <0.5), the former relaxes the accuracyrequirements in Pawlak classical rough set theory, and allows a certain degree ofmisclassification. It enhances the anti-interference ability of the rough set model; Byweakening the equivalence relation, the latter discusses rough set model based on tolerancerelation. The idea of variable precision is introduced into tolerance rough set in this paper.Two variable precision tolerance rough set models (VPTRSM) are proposed. In model Ⅰ,the intersection of lower approximation and boundary region of target concept is not a null set;whereas in model Ⅱthe intersection is null set. Furthermore the properties of lowerapproximation operator and upper approximation operator of VPTRSM are investigated, therelationship between the two models and other rough set models are studied and the reductionis introducted.