Set approximations in fuzzy formal concept analysis

Formal concept analysis and rough set theory are two important tools in knowledge representation and knowledge discovery in relational information systems. The purpose of this paper is to study rough set approximations within formal concept analysis in fuzzy environment. Properties of existent fuzzy concept lattices derived from an adjoint pair of operations are first reviewed and examined. Based on both lattice-theoretic and fuzzy set-theoretic operators, two new pairs of rough fuzzy set approximations within fuzzy formal contexts are then defined. Finally, properties of the rough fuzzy set approximation operators are presented in detail.