We present a new method for constructing and interpreting rough set approximations in an incomplete information table in four steps. Step 1: we introduce the notion of conjunctively definable concepts in a complete table. Step 2: we suggest a slightly different version of Pawlak rough set approximations in a complete table by using the family of conjunctively definable concepts. Step 3: we adapt a possible-world semantics that interprets an incomplete table as a family of complete tables. Correspondingly to conjunctively definable concepts in a complete table, we introduce the notion of conjunctively definable interval concepts in an incomplete table. Step 4: we study rough set approximations in an incomplete table by using the family of conjunctively definable interval concepts. Our method focuses on a conceptual understanding of rough set approximations for the purpose of rule induction. It avoids difficulties with existing approaches with respect to semantical interpretations.
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