Vector quantization and signal compression
Vector quantization and signal compression
Reduction and axiomization of covering generalized rough sets
Information Sciences: an International Journal
A novel approach to fuzzy rough sets based on a fuzzy covering
Information Sciences: an International Journal
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
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
Applications of interval valued t-norms (t-conorms) to fuzzy n-ary sub-hypergroups
Information Sciences: an International Journal
The algebraic structures of generalized rough set theory
Information Sciences: an International Journal
Relationship between generalized rough sets based on binary relation and covering
Information Sciences: an International Journal
A comparison of two types of rough sets induced by coverings
International Journal of Approximate Reasoning
Optimal Boolean Matrix Decomposition: Application to Role Engineering
ICDE '08 Proceedings of the 2008 IEEE 24th International Conference on Data Engineering
On axiomatic characterizations of three pairs of covering based approximation operators
Information Sciences: an International Journal
Discovery of optimal factors in binary data via a novel method of matrix decomposition
Journal of Computer and System Sciences
Deterministic Column-Based Matrix Decomposition
IEEE Transactions on Knowledge and Data Engineering
Generalized lower and upper approximations in a ring
Information Sciences: an International Journal
Rough set theory based on two universal sets and its applications
Knowledge-Based Systems
Invertible approximation operators of generalized rough sets and fuzzy rough sets
Information Sciences: an International Journal
Expert Systems with Applications: An International Journal
A Fast Output-Sensitive Algorithm for Boolean Matrix Multiplication
Algorithmica - Special Issue: European Symposium on Algorithms, Design and Analysis
Rule learning for classification based on neighborhood covering reduction
Information Sciences: an International Journal
The reduction and fusion of fuzzy covering systems based on the evidence theory
International Journal of Approximate Reasoning
Multi-assignment clustering for boolean data
The Journal of Machine Learning Research
Approximations and uncertainty measures in incomplete information systems
Information Sciences: an International Journal
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
Incomplete Multigranulation Rough Set
IEEE Transactions on Systems, Man, and Cybernetics, Part A: Systems and Humans
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
Rough Sets, Coverings and Incomplete Information
Fundamenta Informaticae - Advances in Rough Set Theory
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
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Covering-based rough sets provide an efficient means of dealing with covering data, which occur widely in practical applications. Boolean matrix decomposition has frequently been applied to data mining and machine learning. In this paper, three types of existing covering approximation operators are represented by Boolean matrices, and then used in Boolean matrix decomposition. First, we define two characteristic matrices of a covering. Through these Boolean characteristic matrices, three types of existing covering approximation operator are concisely and equivalently represented. Second, these operator representations are applied to Boolean matrix decomposition, which has a close relationship with nonnegative matrix factorization, a popular and efficient technique for machine learning. We provide a sufficient and necessary condition for a square Boolean matrix to decompose into the Boolean product of another matrix and its transpose. We then develop an algorithm for this Boolean matrix decomposition. Finally, these three covering approximation operators are axiomatized using Boolean matrices. This work presents an interesting viewpoint from which to investigate covering-based rough set theory and its applications.