Monotonic Variable Consistency Rough Set Approaches

摘要

We consider new definitions of Variable Consistency Rough Set Approaches that employ monotonic measures of membership to the approximated set. The monotonicity is understood with respect to the set of considered attributes. This kind of monotonicity is related to the monotonicity of the quality of approximation, considered among basic properties of rough sets. Measures that were employed by approaches proposed so far lack this property. New monotonic measures are considered in two contexts. In the first context, we define Variable Consistency Indiscernibility-based Rough Set Approach (VC-IRSA). In the second context, new measures are applied to Variable Consistency Dominance-based Rough Set Approaches (VC-DRSA). Properties of new definitions are investigated and compared to previously proposed Variable Precision Rough Set (VPRS) model, Rough Bayesian (RB) model and VC-DRSA.