Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
AMAST '95 Proceedings of the 4th International Conference on Algebraic Methodology and Software Technology
Modal-style operators in qualitative data analysis
ICDM '02 Proceedings of the 2002 IEEE International Conference on Data Mining
Topological approaches to covering rough sets
Information Sciences: an International Journal
Granular computing and dual Galois connection
Information Sciences: an International Journal
A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic)
A New Approach to Distributed Algorithms for Reduct Calculation
Transactions on Rough Sets IX
The Princeton Companion to Mathematics
The Princeton Companion to Mathematics
Three-way decisions with probabilistic rough sets
Information Sciences: an International Journal
Transactions on rough sets VI
Characterizing Pawlak's approximation operators
Transactions on rough sets VII
A note on definability and approximations
Transactions on rough sets VII
The superiority of three-way decisions in probabilistic rough set models
Information Sciences: an International Journal
Construction of concept lattices based on indiscernibility matrices
KSEM'06 Proceedings of the First international conference on Knowledge Science, Engineering and Management
Covering based rough set approximations
Information Sciences: an International Journal
Pawlak's Information Systems in Terms of Galois Connections and Functional Dependencies
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Oppositions in rough set theory
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Duality, conjugacy and adjointness of approximation operators in covering-based rough sets
International Journal of Approximate Reasoning
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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.