Four Variable Precision Rough Set Models On Uncertain Space

Variable precision probabilistic rough set model is an effective model in the rough settheory. However, variable precision probabilistic rough set model is based on the probabilitymeasure, which is a class of non-negative set function satisfying additivity. Because thecondition of additivity is too harsh while the equivalence relation in variable precisionprobabilistic rough set model is too strict, the application range of variable precisionprobabilistic rough set model is limited. In order to effectively solve the above problems, onthe bases of the uncertainty measure, the general binary relation and variable precision roughset model, the variable precision rough set model based on equivalence relations on theuncertain space, the variable precision rough set model with the degree based on theuncertainty space, the variable precision rough set model based on similarity relationship onthe uncertainty space, the variable precision rough set model based on the general relationshipon the uncertainty space are proposed. Moreover, the definitions and the properties ofapproximations of four the variable precision rough set models on the uncertain space areprovided. Accordingly, the range of application of the variable precision rough set model isextended.