A novel variable precision (θ, σ) -fuzzy rough set model based on fuzzy granules

Some expanded fuzzy rough set models have been investigated to handle fuzzy databases with uncertain, imprecise and incomplete real-valued information. However, some of them are still sensitive to mislabeled samples and others have only considered relative errors. To remedy these defects, we propose a novel expanded fuzzy rough set model called the variable precision (θ,σ)-fuzzy rough set model based on fuzzy granules. Considering the absolute error limit, we introduce the concept of the variable precision (θ,σ)-fuzzy rough set firstly. Then we present a theorem to ensure that the approximation operators can be calculated efficiently. The basic properties of the model are also investigated, some of which are analogous to those of fuzzy rough sets. Furthermore, the degenerated variable precision (θ,σ)-fuzzy rough set model is shown, and the difference and connection between the degenerated model and the variable precision rough set model introduced by Ziarko are studied. Finally, the definitions of β-fuzzy lower and upper approximation reducts are presented and the attribute reduction methods are proposed.