Rough set model based on formal concept analysis

This paper proposes a rough set model based on formal concept analysis. In this model, a solution to an algebraic structure problem is first provided in an information system: a lattice structure is inferred from the information system and corresponding nodes are called rough concepts. How to deal with common problems in rough set theory based on rough concepts is then explored, such as upper and lower approximation operators, reducts and cores. Decision dependency has become a common form of knowledge representation owing to its properties of expressiveness and ease of understanding, so it has been widely used in practice. Finally, application of rough concepts to the extraction of decision dependencies from a decision table is studied; a complete and non-redundant set of decision dependencies can be obtained from a decision table. Examples demonstrate that application of the method presented in this paper is valid and practicable. The results not only provide a better understanding of rough set theory from the perspective of formal concept analysis, but also demonstrate a new way of combining rough set theory and formal concept analysis.