Fuzzy Sets and Systems
Logic and discrete mathematics: a computer science perspective
Logic and discrete mathematics: a computer science perspective
Information Sciences: an International Journal
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Approximate Operators: Axiomatic Rough Set Theory
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
On the structure of rough approximations
Fundamenta Informaticae
Generalized rough sets over fuzzy lattices
Information Sciences: an International Journal
Axiomatic systems for rough sets and fuzzy rough sets
International Journal of Approximate Reasoning
The algebraic structures of generalized rough set theory
Information Sciences: an International Journal
Relationship between generalized rough sets based on binary relation and covering
Information Sciences: an International Journal
An Equivalent Definition of Rough Sets
RSCTC '08 Proceedings of the 6th International Conference on Rough Sets and Current Trends in Computing
A comparison of two types of rough sets induced by coverings
International Journal of Approximate Reasoning
Relationship among basic concepts in covering-based rough sets
Information Sciences: an International Journal
An axiomatic approach of fuzzy rough sets based on residuated lattices
Computers & Mathematics with Applications
Rough set theory based on two universal sets and its applications
Knowledge-Based Systems
Invertible approximation operators of generalized rough sets and fuzzy rough sets
Information Sciences: an International Journal
Characterizing Pawlak's approximation operators
Transactions on rough sets VII
Covering rough sets based on neighborhoods: An approach without using neighborhoods
International Journal of Approximate Reasoning
Neighborhood rough sets based matrix approach for calculation of the approximations
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
International Journal of Approximate Reasoning
The fourth type of covering-based rough sets
Information Sciences: an International Journal
An Axiomatic Approach to the Roughness Measure of Rough Sets
Fundamenta Informaticae
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The theory of rough sets deals with the approximation of an arbitrary subset of a universe by two definable or observable subsets called, respectively, the lower and the upper approximation. There are at least two methods for the development of this theory, the constructive and the axiomatic approaches. The rough set axiomatic system is the foundation of rough sets theory. This paper proposes a new matrix view of the theory of rough sets, we start with a binary relation and we redefine a pair of lower and upper approximation operators using the matrix representation. Different classes of rough set algebras are obtained from different types of binary relations. Various classes of rough set algebras are characterized by different sets of axioms. Axioms of upper approximation operations guarantee the existence of certain types of binary relations (or matrices) producing the same operators. The upper approximation of the Pawlak rough sets, rough fuzzy sets and rough sets of vectors over an arbitrary fuzzy lattice are characterized by the same independent axiomatic system.