Tolerance approximation spaces
Fundamenta Informaticae - Special issue: rough sets
Extensions and intentions in the rough set theory
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
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
Using Rough Sets with Heuristics for Feature Selection
Journal of Intelligent Information Systems
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
A Generalized Definition of Rough Approximations Based on Similarity
IEEE Transactions on Knowledge and Data Engineering
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
Information Sciences—Informatics and Computer Science: An International Journal
Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
Peculiarity Oriented Multidatabase Mining
IEEE Transactions on Knowledge and Data Engineering
Constructive and axiomatic approaches of fuzzy approximation operators
Information Sciences—Informatics and Computer Science: An International Journal - Mining stream data
Two new operators in rough set theory with applications to fuzzy sets
Information Sciences—Informatics and Computer Science: An International Journal
On the abstraction of conventional dynamic systems: from numerical analysis to linguistic analysis
Information Sciences—Informatics and Computer Science: An International Journal
Properties of the Fourth Type of Covering-Based Rough Sets
HIS '06 Proceedings of the Sixth International Conference on Hybrid Intelligent Systems
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
Topological approaches to covering rough sets
Information Sciences: an International Journal
The Axiomatization of the Rough Set Upper Approximation Operations
Fundamenta Informaticae
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
On Three Types of Covering-Based Rough Sets
IEEE Transactions on Knowledge and Data Engineering
Generalized rough sets over fuzzy lattices
Information Sciences: an International Journal
On generalized intuitionistic fuzzy rough approximation operators
Information Sciences: an International Journal
On the topological properties of fuzzy rough sets
Fuzzy Sets and Systems
On the structure of generalized rough sets
Information Sciences: an International Journal
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
Granular computing: structures, representations, and applications
RSFDGrC'03 Proceedings of the 9th international conference on Rough sets, fuzzy sets, data mining, and granular computing
Binary relation based rough sets
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
Covering-Based generalized rough fuzzy sets
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
Axiomatic systems of generalized rough sets
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
Covering based granular computing for conflict analysis
ISI'06 Proceedings of the 4th IEEE international conference on Intelligence and Security Informatics
Rough approximation operators in covering approximation spaces
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Algebraic structures for rough sets
Transactions on Rough Sets II
Information Sciences: an International Journal
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy Systems
An Interval-Valued Intuitionistic Fuzzy Rough Set Model
Fundamenta Informaticae
Generalized lower and upper approximations in a ring
Information Sciences: an International Journal
Poset approaches to covering-based rough sets
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Covering rough sets based on neighborhoods: An approach without using neighborhoods
International Journal of Approximate Reasoning
A comparison of two kinds of definitions of rough approximations based on a similarity relation
Information Sciences: an International Journal
Rough sets and general basic set assignments
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Covering numbers in covering-based rough sets
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Covering rough set model based on multi-granulations
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Transversal and function matroidal structures of covering-based rough sets
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Bipartite graphs and coverings
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Rough approximations in general approximation spaces
IUKM'11 Proceedings of the 2011 international conference on Integrated uncertainty in knowledge modelling and decision making
Textures and covering based rough sets
Information Sciences: an International Journal
Multi knowledge based rough approximations and applications
Knowledge-Based Systems
Entropy and co-entropy of a covering approximation space
International Journal of Approximate Reasoning
Generalized intuitionistic fuzzy rough sets based on intuitionistic fuzzy coverings
Information Sciences: an International Journal
Covering based rough set approximations
Information Sciences: an International Journal
The fourth type of covering-based rough sets
Information Sciences: an International Journal
Topological characterizations of covering for special covering-based upper approximation operators
Information Sciences: an International Journal
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
An Axiomatic Approach to the Roughness Measure of Rough Sets
Fundamenta Informaticae
An Interval-Valued Intuitionistic Fuzzy Rough Set Model
Fundamenta Informaticae
Bipolar fuzzy rough set model on two different universes and its application
Knowledge-Based Systems
Quantitative analysis for covering-based rough sets through the upper approximation number
Information Sciences: an International Journal
Related family: A new method for attribute reduction of covering information systems
Information Sciences: an International Journal
Rough matroids based on relations
Information Sciences: an International Journal
Multigranulation rough sets: From partition to covering
Information Sciences: an International Journal
Approximation operators on complete completely distributive lattices
Information Sciences: an International Journal
Four matroidal structures of covering and their relationships with rough sets
International Journal of Approximate Reasoning
International Journal of Approximate Reasoning
Minimal Description and Maximal Description in Covering-based Rough Sets
Fundamenta Informaticae
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Uncertainty and incompleteness of knowledge are widespread phenomena in information systems. Rough set theory is a tool for dealing with granularity and vagueness in data analysis. Rough set method has already been applied to various fields such as process control, economics, medical diagnosis, biochemistry, environmental science, biology, chemistry, psychology, and conflict analysis. Covering-based rough set theory is an extension to classical rough sets. In covering-based rough sets, there exist several basic concepts such as reducible elements of a covering, minimal descriptions, unary coverings, and the property that the intersection of any two elements is the union of finite elements in this covering. These concepts appeared in the literature of covering-based rough sets separately. In this paper we study the relationships between them. In particular, we establish the equivalence of the unary covering and the covering with the property that the intersection of any two elements is the union of finite elements in this covering. We also investigate the relationship between the covering lower approximation operation and the interior operator. A characterization of the interior operator by the covering lower approximation operation is presented in this paper. Correspondingly, we study the relationship between the covering upper approximation operation and the closure operator. In addition, we explore the conditions under which the covering upper approximation operation is monotone. The study of the relationships between these concepts will help us have a better understanding of covering-based rough sets.