Duality in Rough Set Theory Based on the Square of Opposition

In rough set theory, one typically considers pairs of dual entities such as a pair of lower and upper approximations, a pair of indiscernibility and discernibility relations, a pair of sets of core and non-useful attributes, and several more. By adopting a framework known as hypercubes of duality, of which the square of opposition is a special case, this paper investigates the role of duality for interpreting fundamental concepts in rough set analysis. The objective is not to introduce new concepts, but to revisit the existing concepts by casting them in a common framework so that we can obtain more insights into an understanding of these concepts and their relationships. We demonstrate that these concepts can, in fact, be defined and explained in a common framework, although they first appear to be very different and have been studied in somewhat isolated ways.