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
Relational interpretations of neighborhood operators and rough set approximation operators
Information Sciences—Informatics and Computer Science: An International Journal
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
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
Logical Properties of Rough Sets
HPC '00 Proceedings of the The Fourth International Conference on High-Performance Computing in the Asia-Pacific Region-Volume 2 - Volume 2
Fuzzy logic = computing with words
IEEE Transactions on Fuzzy 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
Uncertainty Measure of Covering Generated Rough Set
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
A novel approach to fuzzy rough sets based on a fuzzy covering
Information Sciences: an International Journal
Information Sciences: an International Journal
On Three Types of Covering-Based Rough Sets
IEEE Transactions on Knowledge and Data Engineering
Minimization of axiom sets on fuzzy approximation operators
Information Sciences: an International Journal
On definable concepts of rough set models
Information Sciences: an International Journal
Learning fuzzy rules from fuzzy samples based on rough set technique
Information Sciences: an International Journal
Measures for evaluating the decision performance of a decision table in rough set theory
Information Sciences: an International Journal
A multiview approach for intelligent data analysis based on data operators
Information Sciences: an International Journal
Attribute reduction based on evidence theory in incomplete decision systems
Information Sciences: an International Journal
Generalized rough sets over fuzzy lattices
Information Sciences: an International Journal
Information Sciences: an International Journal
A systematic study on attribute reduction with rough sets based on general binary relations
Information Sciences: an International Journal
The lower and upper approximations in a quotient hypermodule with respect to fuzzy sets
Information Sciences: an International Journal
On generalized intuitionistic fuzzy rough approximation operators
Information Sciences: an International Journal
On the evaluation of the decision performance of an incomplete decision table
Data & Knowledge Engineering
Approximations and reducts with covering generalized rough sets
Computers & Mathematics with Applications
Generalized fuzzy rough approximation operators based on fuzzy coverings
International Journal of Approximate Reasoning
Axiomatic systems for rough sets and fuzzy rough sets
International Journal of Approximate Reasoning
On fuzzy approximation operators in attribute reduction with fuzzy rough sets
Information Sciences: an International Journal
Measures of general fuzzy rough sets on a probabilistic space
Information Sciences: an International Journal
Neighborhood rough set based heterogeneous feature subset selection
Information Sciences: an International Journal
Consistency measure, inclusion degree and fuzzy measure in decision tables
Fuzzy Sets and Systems
The algebraic structures of generalized rough set theory
Information Sciences: an International Journal
RSEISP '07 Proceedings of the international conference on Rough Sets and Intelligent Systems Paradigms
Review: Dimensionality reduction based on rough set theory: A review
Applied Soft Computing
Relationship between generalized rough sets based on binary relation and covering
Information Sciences: an International Journal
Discernibility matrix simplification for constructing attribute reducts
Information Sciences: an International Journal
On characterization of intuitionistic fuzzy rough sets based on intuitionistic fuzzy implicators
Information Sciences: an International Journal
Fuzzy-rough attribute reduction via mutual information with an application to cancer classification
Computers & Mathematics with Applications
A comparison of two types of rough sets induced by coverings
International Journal of Approximate Reasoning
Approaches to knowledge reduction of covering decision systems based on information theory
Information Sciences: an International Journal
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
Information Sciences: an International Journal
Knowledge Reduction of Covering Approximation Space
Transactions on Computational Science V
On Covering Based Approximations of Classifications of Sets
IEA/AIE '09 Proceedings of the 22nd International Conference on Industrial, Engineering and Other Applications of Applied Intelligent Systems: Next-Generation Applied Intelligence
Rough 3-Valued Łukasiewicz Agebras and MV-Algebras
RSKT '09 Proceedings of the 4th International Conference on Rough Sets and Knowledge 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
Adapted variable precision rough set approach for EEG analysis
Artificial Intelligence in Medicine
On axiomatic characterizations of three pairs of covering based approximation operators
Information Sciences: an International Journal
On some properties of covering based approximations of classifications of sets
Proceedings of the 2nd International Conference on Interaction Sciences: Information Technology, Culture and Human
Rough neuro-fuzzy structures for classification with missing data
IEEE Transactions on Systems, Man, and Cybernetics, Part B: Cybernetics
An Interval-Valued Intuitionistic Fuzzy Rough Set Model
Fundamenta Informaticae
Generalized lower and upper approximations in a ring
Information Sciences: an International Journal
Reduction about approximation spaces of covering generalized rough sets
International Journal of Approximate Reasoning
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
On transitive uncertainty mappings
RSKT'07 Proceedings of the 2nd international conference on Rough sets and knowledge technology
A note on definability and approximations
Transactions on rough sets VII
Approximation reduction in inconsistent incomplete decision tables
Knowledge-Based Systems
Information Sciences: an International Journal
Rough implication operator based on strong topological rough algebras
Information Sciences: an International Journal
An application of covering approximation spaces on network security
Computers & Mathematics with Applications
Poset approaches to covering-based rough sets
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
A robust fuzzy rough set model based on minimum enclosing ball
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Temporal dynamics in rough sets based on coverings
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
Extension of covering approximation space and its application in attribute reduction
RSKT'10 Proceedings of the 5th international conference on Rough set and knowledge technology
An efficient classifier design integrating rough set and set oriented database operations
Applied Soft Computing
Covering rough sets based on neighborhoods: An approach without using neighborhoods
International Journal of Approximate Reasoning
Data compression with homomorphism in covering information systems
International Journal of Approximate Reasoning
Axiomatization and conditions for neighborhoods in a covering to form a partition
Information Sciences: an International Journal
A comparison of two kinds of definitions of rough approximations based on a similarity relation
Information Sciences: an International Journal
On minimization of axiom sets characterizing covering-based approximation operators
Information Sciences: an International Journal
On lower and upper intension order relations by different cover concepts
Information Sciences: an International Journal
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
Accumulated cost based test-cost-sensitive attribute reduction
RSFDGrC'11 Proceedings of the 13th international conference on Rough sets, fuzzy sets, data mining and granular computing
Attribute reduction in incomplete information systems
AICI'11 Proceedings of the Third international conference on Artificial intelligence and computational intelligence - Volume Part III
Rule learning for classification based on neighborhood covering reduction
Information Sciences: an International Journal
Optimal sub-reducts with test cost constraint
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Partitions, coverings, reducts and rule learning in rough set theory
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
A variable precision covering generalized rough set model
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
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
The reduction and fusion of fuzzy covering systems based on the evidence theory
International Journal of Approximate Reasoning
Approximation operators based on vague relations and roughness measures of vague sets
Frontiers of Computer Science in China
On reduction of morphological covering rough sets
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
Binary relation based rough sets
FSKD'06 Proceedings of the Third international conference on Fuzzy Systems and Knowledge Discovery
Rough sets and brouwer-zadeh lattices
RSKT'06 Proceedings of the First international conference on Rough Sets and Knowledge Technology
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
Applying indiscernibility attribute sets to knowledge reduction
AI'05 Proceedings of the 18th Australian Joint conference on Advances in Artificial Intelligence
Covering based granular computing for conflict analysis
ISI'06 Proceedings of the 4th IEEE international conference on Intelligence and Security Informatics
Expanding tolerance RST models based on cores of maximal compatible blocks
RSCTC'06 Proceedings of the 5th international conference on Rough Sets and Current Trends in Computing
Topological structure of generalized rough sets
Computers & Mathematics with Applications
Roughness based on fuzzy ideals
Information Sciences: an International Journal
Information Sciences: an International Journal
Entropy and co-entropy of a covering approximation space
International Journal of Approximate Reasoning
Bayesian rough set model: A further investigation
International Journal of Approximate Reasoning
Test cost constraint reduction with common cost
FGIT'11 Proceedings of the Third international conference on Future Generation Information Technology
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
Graded rough set model based on two universes and its properties
Knowledge-Based Systems
Test-cost-sensitive attribute reduction
Information Sciences: an International Journal
Attribute reduction of data with error ranges and test costs
Information Sciences: an International Journal
NMGRS: Neighborhood-based multigranulation rough sets
International Journal of Approximate Reasoning
Communication between information systems with covering based rough sets
Information Sciences: an International Journal
An Axiomatic Approach to the Roughness Measure of Rough Sets
Fundamenta Informaticae
Attribute Reduction in Formal Contexts: A Covering Rough Set Approach
Fundamenta Informaticae - Knowledge Technology
An Interval-Valued Intuitionistic Fuzzy Rough Set Model
Fundamenta Informaticae
A competition strategy to cost-sensitive decision trees
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Topological properties of the pessimistic multigranulation rough set model
RSKT'12 Proceedings of the 7th international conference on Rough Sets and Knowledge Technology
Topological and lattice structures of L-fuzzy rough sets determined by lower and upper sets
Information Sciences: an International Journal
Soft Minimum-Enclosing-Ball Based Robust Fuzzy Rough Sets
Fundamenta Informaticae - Rough Sets and Knowledge Technology (RSKT 2010)
Attribute Reduction Using Extension of Covering Approximation Space
Fundamenta Informaticae - Rough Sets and Knowledge Technology (RSKT 2010)
On the structure of the multigranulation rough set model
Knowledge-Based Systems
Matroidal structure of rough sets and its characterization to attribute reduction
Knowledge-Based Systems
Feature selection using rough entropy-based uncertainty measures in incomplete decision systems
Knowledge-Based Systems
Quantitative analysis for covering-based rough sets through the upper approximation number
Information Sciences: an International Journal
Studies on the covering rough set and its matrix description
AICI'12 Proceedings of the 4th international conference on Artificial Intelligence and Computational Intelligence
Relationships between covering-based rough sets and relation-based rough sets
Information Sciences: an International Journal
A matroidal approach to rough set theory
Theoretical Computer Science
Related family: A new method for attribute reduction of covering information systems
Information Sciences: an International Journal
Granular association rule mining through parametric rough sets
BI'12 Proceedings of the 2012 international conference on Brain Informatics
Rough matroids based on relations
Information Sciences: an International Journal
Decision rule mining using classification consistency rate
Knowledge-Based Systems
Approximation operators on complete completely distributive lattices
Information Sciences: an International Journal
Quick attribute reduction in inconsistent decision tables
Information Sciences: an International Journal
A novel method for attribute reduction of covering decision systems
Information Sciences: an International Journal
Four matroidal structures of covering and their relationships with rough sets
International Journal of Approximate Reasoning
An extension to rough c-means clustering algorithm based on boundary area elements discrimination
Transactions on Rough Sets XVI
The concept of reducts in pawlak three-step rough set analysis
Transactions on Rough Sets XVI
Approximation of sets based on partial covering
Transactions on Rough Sets XVI
Rule acquisition and complexity reduction in formal decision contexts
International Journal of Approximate Reasoning
An axiomatic characterization of probabilistic rough sets
International Journal of Approximate Reasoning
Feature selection with test cost constraint
International Journal of Approximate Reasoning
Duality, conjugacy and adjointness of approximation operators in covering-based rough sets
International Journal of Approximate Reasoning
Nullity-based matroid of rough sets and its application to attribute reduction
Information Sciences: an International Journal
Characteristic matrix of covering and its application to Boolean matrix decomposition
Information Sciences: an International Journal
Reductions and Saturation Reductions of (Abstract) Knowledge Bases
Electronic Notes in Theoretical Computer Science (ENTCS)
A Comparative Study of Ordered and Covering Information Systems
Fundamenta Informaticae
Minimal Description and Maximal Description in Covering-based Rough Sets
Fundamenta Informaticae
Covering-based rough fuzzy sets and binary relation
Journal of Intelligent & Fuzzy Systems: Applications in Engineering and Technology
Hi-index | 0.07 |
This paper investigates some basic properties of covering generalized rough sets, and their comparison with the corresponding ones of Pawlak's rough sets, a tool for data mining. The focus here is on the concepts and conditions for two coverings to generate the same covering lower approximation or the same covering upper approximation. The concept of reducts of coverings is introduced and the procedure to find a reduct for a covering is given. It has been proved that the reduct of a covering is the minimal covering that generates the same covering lower approximation or the same covering upper approximation, so this concept is also a technique to get rid of redundancy in data mining. Furthermore, it has been shown that covering lower and upper approximations determine each other. Finally, a set of axioms is constructed to characterize the covering lower approximation operation.