In a formal context, the lower and upper approximations of an arbitrary set of objects are constructed by object-oriented concepts, attribute-oriented concepts, approximable concepts and weak approximable concepts, respectively. We first define the concept of approximations based on lattice-theoretic operators, and the properties of them are discussed. In order to overcome the two shortcomings in the former approximations, we present the concept of approximations based on set-theoretic operators.The study can help further understanding of data analysis using rough set theory and formal concept analysis.
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