The two sides of the theory of rough sets

There exist two formulations of the theory of rough sets. A conceptual formulation emphasizes on the meaning and interpretation of the concepts and notions of the theory, whereas a computational formulation focuses on procedures and algorithms for constructing these notions. Except for a few earlier studies, computational formulations dominate research in rough sets. In this paper, we argue that an oversight of conceptual formulations makes an in-depth understanding of rough set theory very difficult. The conceptual and computational formulations are the two sides of the same coin; it is essential to pay equal, if not more, attention to conceptual formulations. As a demonstration, we examine and compare conceptual and computational formulations of two fundamental concepts of rough sets, namely, approximations and reducts.