Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches
IEEE Transactions on Knowledge and Data Engineering
Mining top-K covering rule groups for gene expression data
Proceedings of the 2005 ACM SIGMOD international conference on Management of data
Topological approaches to covering rough sets
Information Sciences: an International Journal
Information Sciences: an International Journal
Fuzzy rough set theory for the interval-valued fuzzy information systems
Information Sciences: an International Journal
Neighborhood rough set based heterogeneous feature subset selection
Information Sciences: an International Journal
Rough sets approach to symbolic value partition
International Journal of Approximate Reasoning
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
Information Sciences: an International Journal
On axiomatic characterizations of three pairs of covering based approximation operators
Information Sciences: an International Journal
On the topological properties of fuzzy rough sets
Fuzzy Sets and Systems
Data compression with homomorphism in covering information systems
International Journal of Approximate Reasoning
A Boolean function approach to feature selection in consistent decision information systems
Expert Systems with Applications: An International Journal
Fuzzy rough granular neural networks, fuzzy granules, and classification
Theoretical Computer Science
Approximation of sets based on partial covering
Theoretical Computer Science
Transversal and function matroidal structures of covering-based rough sets
RSKT'11 Proceedings of the 6th international conference on Rough sets and knowledge technology
Matroidal approaches to rough sets via closure operators
International Journal of Approximate Reasoning
Rough set theory applied to lattice theory
Information Sciences: an International Journal
Covering based rough set approximations
Information Sciences: an International Journal
On some types of neighborhood-related covering rough sets
International Journal of Approximate Reasoning
Test-cost-sensitive attribute reduction
Information Sciences: an International Journal
Generalization of Pawlak's rough approximation spaces by using δβ-open sets
International Journal of Approximate Reasoning
Entropies and Co-Entropies of Coverings with Application to Incomplete Information Systems
Fundamenta Informaticae - New Frontiers in Scientific Discovery - Commemorating the Life and Work of Zdzislaw Pawlak
Matroidal structure of rough sets and its characterization to attribute reduction
Knowledge-Based Systems
Quantitative analysis for covering-based rough sets through the upper approximation number
Information Sciences: an International Journal
Nullity-based matroid of rough sets and its application to attribute reduction
Information Sciences: an International Journal
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Covering is a common form of data representation, and covering-based rough sets serve as an efficient technique to process this type of data. However, many important problems such as covering reduction in covering-based rough sets are NP-hard so that most algorithms to solve them are greedy. Matroids provide well-established platforms for greedy algorithm foundation and implementation. Therefore, it is necessary to integrate covering-based rough set with matroid. In this paper, we propose four matroidal structures of coverings and establish their relationships with rough sets. First, four different viewpoints are presented to construct these four matroidal structures of coverings, including 1-rank matroids, bigraphs, upper approximation numbers and transversals. The respective advantages of these four matroidal structures to rough sets are explored. Second, the connections among these four matroidal structures are studied. It is interesting to find that they coincide with each other. Third, a converse view is provided to induce a covering by a matroid. We study the relationship between this induction and the one from a covering to a matroid. Finally, some important concepts of covering-based rough sets, such as approximation operators, are equivalently formulated by these matroidal structures. These interesting results demonstrate the potential to combine covering-based rough sets with matroids.