Fuzzy Sets and Systems
Information Sciences: an International Journal
Extensions and intentions in the rough set theory
Information Sciences: an International Journal
Axiomatics for fuzzy rough sets
Fuzzy Sets and Systems
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
A Handwritten Numeral Character Classification Using Tolerant Rough Set
IEEE Transactions on Pattern Analysis and Machine Intelligence
A comparative study of fuzzy rough sets
Fuzzy Sets and Systems
A Generalized Definition of Rough Approximations Based on Similarity
IEEE Transactions on Knowledge and Data Engineering
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
Algebraic Structures of Rough Sets
RSKD '93 Proceedings of the International Workshop on Rough Sets and Knowledge Discovery: Rough Sets, Fuzzy Sets and Knowledge Discovery
An axiomatic characterization of a fuzzy generalization of rough sets
Information Sciences—Informatics and Computer Science: An International Journal
Constructive and axiomatic approaches of fuzzy approximation operators
Information Sciences—Informatics and Computer Science: An International Journal - Mining stream data
Topological approaches to covering rough sets
Information Sciences: an International Journal
Information Sciences: an International Journal
Construction of rough approximations in fuzzy setting
Fuzzy Sets and Systems
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
Generalized fuzzy rough sets determined by a triangular norm
Information Sciences: an International Journal
The algebraic structures of generalized rough set theory
Information Sciences: an International Journal
A comparison of two types of rough sets induced by coverings
International Journal of Approximate Reasoning
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
A comparative study of fuzzy sets and rough sets
Information Sciences: an International Journal
Granular computing: structures, representations, and applications
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
On minimization of axiom sets characterizing covering-based approximation operators
Information Sciences: an International Journal
A comparative study of rough sets for hybrid data
Information Sciences: an International Journal
Multi-adjoint property-oriented and object-oriented concept lattices
Information Sciences: an International Journal
Generalized approximations defined by non-equivalence relations
Information Sciences: an International Journal
Rough set-based approach for modeling relationship measures in product planning
Information Sciences: an International Journal
Covering based rough set approximations
Information Sciences: an International Journal
Extended rough set-based attribute reduction in inconsistent incomplete decision systems
Information Sciences: an International Journal
On the generalization of fuzzy rough sets
IEEE Transactions on Fuzzy Systems
Relationships among generalized rough sets in six coverings and pure reflexive neighborhood system
Information Sciences: an International Journal
Rough sets in the Soft Computing environment
Information Sciences: an International Journal
Information-theoretic measures associated with rough set approximations
Information Sciences: an International Journal
Attribute reduction of data with error ranges and test costs
Information Sciences: an International Journal
A general frame for intuitionistic fuzzy rough sets
Information Sciences: an International Journal
The Axiomatization of the Rough Set Upper Approximation Operations
Fundamenta Informaticae
Rough set approach to incomplete numerical data
Information Sciences: an International Journal
A novel method for attribute reduction of covering decision systems
Information Sciences: an International Journal
Pessimistic rough set based decisions: A multigranulation fusion strategy
Information Sciences: an International Journal
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Axiomatic approaches are important for understanding the concepts of rough set theory. The properties of the approximation operators constructed in rough set theory are determined by a binary relation. A linkage, in the form of a necessary and sufficient condition, between the constructive approach and an axiomatic system is established in this paper. Various classes of rough set algebras are characterized by different sets of axioms. With no restriction on the cardinality of the universal set, we use only one axiom to describe the approximation generated by the reflexive, symmetric, and transitive relations, respectively. In addition, we characterize lower and upper approximations of the Pawlak rough set with only one axiom. We also study a similar problem in the context of fuzzy sets.