Axiomatics for fuzzy rough sets
Fuzzy Sets and Systems
Rough set methods and applications: new developments in knowledge discovery in information systems
Rough set methods and applications: new developments in knowledge discovery in information systems
Rough Sets: Theoretical Aspects of Reasoning about Data
Rough Sets: Theoretical Aspects of Reasoning about Data
Machine Learning
A comparative study of fuzzy rough sets
Fuzzy Sets and Systems
Information Sciences—Informatics and Computer Science: An International Journal
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
Learning with non-positive kernels
ICML '04 Proceedings of the twenty-first international conference on Machine learning
Semantics-Preserving Dimensionality Reduction: Rough and Fuzzy-Rough-Based Approaches
IEEE Transactions on Knowledge and Data Engineering
Feature Space Interpretation of SVMs with Indefinite Kernels
IEEE Transactions on Pattern Analysis and Machine Intelligence
On fuzzy-rough sets approach to feature selection
Pattern Recognition Letters
Information-preserving hybrid data reduction based on fuzzy-rough techniques
Pattern Recognition Letters
A novel approach to fuzzy rough sets based on a fuzzy covering
Information Sciences: an International Journal
On Representing and Generating Kernels by Fuzzy Equivalence Relations
The Journal of Machine Learning Research
Minimization of axiom sets on fuzzy approximation operators
Information Sciences: an International Journal
Rough fuzzy approximations on two universes of discourse
Information Sciences: an International Journal
Generalized rough sets over fuzzy lattices
Information Sciences: an International Journal
Discernibility matrix simplification for constructing attribute reducts
Information Sciences: an International Journal
Kernel Discriminant Analysis for Positive Definite and Indefinite Kernels
IEEE Transactions on Pattern Analysis and Machine Intelligence
Attribute selection with fuzzy decision reducts
Information Sciences: an International Journal
New approaches to fuzzy-rough feature selection
IEEE Transactions on Fuzzy Systems
FRSVMs: Fuzzy rough set based support vector machines
Fuzzy Sets and Systems
Fuzzy-rough data reduction with ant colony optimization
Fuzzy Sets and Systems
Gaussian kernel based fuzzy rough sets: Model, uncertainty measures and applications
International Journal of Approximate Reasoning
Local reduction of decision system with fuzzy rough sets
Fuzzy Sets and Systems
Computers and Electronics in Agriculture
Granular computing based on fuzzy similarity relations
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue on Recent advances on machine learning and Cybernetics
On the generalization of fuzzy rough sets
IEEE Transactions on Fuzzy Systems
Fuzzy-Rough Sets Assisted Attribute Selection
IEEE Transactions on Fuzzy Systems
Attributes Reduction Using Fuzzy Rough Sets
IEEE Transactions on Fuzzy Systems
Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets
Information Sciences: an International Journal
Sample Pair Selection for Attribute Reduction with Rough Set
IEEE Transactions on Knowledge and Data Engineering
Structure of feature spaces related to fuzzy similarity relations as kernels
Fuzzy Sets and Systems
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Fuzzy rough sets are a generalization of crisp rough sets for measuring inconsistency between conditional attributes and decision attributes for many decision systems. In many classification problems a membership function for the training sample belonging to a certain class can be computed by methods in fuzzy rough sets. In this paper, we present a geometrical interpretation and its applications of this kind of membership functions. First, we prove that every fuzzy similarity relation in fuzzy rough sets is a reproducing kernel which is related to a Krein space, thus, fuzzy similarity relations can be geometrically explained in a Krein space. Second, we will present the interpretation of several types of membership functions geometrically by using the lower approximations in fuzzy rough sets, in terms of square distances in Krein spaces. As practical applications of these membership functions, we develop a new algorithm to find reducts and reformulate soft margin support vector machines by taking the membership degree for every training sample into considerations. Experimental results also demonstrate the effectiveness of the work proposed in this paper.