Extensions and intentions in the rough set theory
Information Sciences: an International Journal
Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
Properties of the Second Type of Covering-Based Rough Sets
WI-IATW '06 Proceedings of the 2006 IEEE/WIC/ACM international conference on Web Intelligence and Intelligent Agent Technology
A novel approach to fuzzy rough sets based on a fuzzy covering
Information Sciences: an International Journal
Properties of the First Type of Covering-Based Rough Sets
ICDMW '06 Proceedings of the Sixth IEEE International Conference on Data Mining - Workshops
Information Sciences: an International Journal
On Three Types of Covering-Based Rough Sets
IEEE Transactions on Knowledge and Data Engineering
Measuring roughness of generalized rough sets induced by a covering
Fuzzy Sets and Systems
Relationship between generalized rough sets based on binary relation and covering
Information Sciences: an International Journal
Logics from Galois connections
International Journal of Approximate Reasoning
A Geometry of Approximation: Rough Set Theory Logic, Algebra and Topology of Conceptual Patterns (Trends in Logic)
A New Type of Covering Approximation Operators
ICECT '09 Proceedings of the 2009 International Conference on Electronic Computer Technology
Knowledge Reduction in Formal Contexts Based on Covering Rough Sets
RSKT '09 Proceedings of the 4th International Conference on Rough Sets and Knowledge Technology
On axiomatic characterizations of three pairs of covering based approximation operators
Information Sciences: an International Journal
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
Reduction about approximation spaces of covering generalized rough sets
International Journal of Approximate Reasoning
On generalizing rough set theory
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
The reduction and fusion of fuzzy covering systems based on the evidence theory
International Journal of Approximate Reasoning
Binary relation based rough sets
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
Entropy and co-entropy of a covering approximation space
International Journal of Approximate Reasoning
Covering based rough set approximations
Information Sciences: an International Journal
Fuzzy Rough Sets: The Forgotten Step
IEEE Transactions on Fuzzy Systems
On some types of neighborhood-related covering rough sets
International Journal of Approximate Reasoning
Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system
Information Sciences: an International Journal
Rough Sets, Coverings and Incomplete Information
Fundamenta Informaticae - Advances in Rough Set Theory
Oppositions in rough set theory
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Duality in Rough Set Theory Based on the Square of Opposition
Fundamenta Informaticae - To Andrzej Skowron on His 70th Birthday
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Many different proposals exist for the definition of lower and upper approximation operators in covering-based rough sets. In this paper, we establish relationships between the most commonly used operators, using especially concepts of duality, conjugacy and adjointness (also referred to as Galois connection). We highlight the importance of the adjointness condition as a way to provide a meaningful link, aside from duality, between a pair of approximation operators. Moreover, we show that a pair of a lower and an upper approximation operator can be dual and adjoint at the same time if and only if the upper approximation is self-conjugate, and we relate this result to a similar characterization obtained for the generalized rough set model based on a binary relation.