Affiliations: Department of Computer Science, University of Regina, Regina, Canada. yyao@cs.uregina.ca
Note: [] Address for correspondence: Department of Computer Science, University of Regina, Regina, Saskatchewan, Canada S4S 0A2 On this very special occasion of the seventieth birthday celebration of Professor Andrzej Skowron, I would like to thank Andrzej for his many years of friendship and support. I appreciate very much Andrzej's wisdom of living and researching that I have learned from his writings and many conversations with him. This work is partially supported by a Discovery Grant from NSERC Canada. The author thanks Dominik Ślęzak for the encouragement and the reviewers for their constructive comments.
Abstract: 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.
Keywords: Core attributes, useful and non-useful attributes, duality, hypercubes of duality, indiscernibility and discernibility relations and matrices, lower and upper approximations, square of opposition
