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
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
Constructive and algebraic methods of the theory of rough sets
Information Sciences: an International Journal
On the Structure of Rough Approximations
Fundamenta Informaticae
Multi knowledge based rough approximations and applications
Knowledge-Based Systems
Using one axiom to characterize rough set and fuzzy rough set approximations
Information Sciences: an International Journal
AICI'12 Proceedings of the 4th international conference on Artificial Intelligence and Computational Intelligence
Approximations in Rough Sets vs Granular Computing for Coverings
International Journal of Cognitive Informatics and Natural Intelligence
Composite rough sets for dynamic data mining
Information Sciences: an International Journal
Minimal Description and Maximal Description in Covering-based 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.