Rough-set concept analysis: Interpreting RS-definable concepts based on ideas from formal concept analysis

Based on ideas from formal concept analysis, this paper interprets the notions of RS-definable concepts (i.e., rough-set definable concepts) and the Boolean algebra of RS-definable concepts. We explicitly represent a RS-definable concept as a pair of an extension and an intension, where the extension is a set of objects and the intension is a family of sets of attribute-value pairs called avp-sets. An object in the extension satisfies at least one avp-set in the intension and each avp-set in the intension is satisfied by only objects in the extension. The two-directional connections produce an atomic Boolean algebra of RS-definable concepts, corresponding to the lattice of formal concepts in formal concept analysis. The Boolean algebra of RS-definable concepts is used to define and interpret a subset of objects through a pair of lower and upper approximations. The new formulation emphasizes on an in-depth conceptual understanding of rough-set concept analysis.