Axiomatics for fuzzy rough sets
Fuzzy Sets and Systems
An axiomatic characterization of a fuzzy generalization of rough sets
Information Sciences—Informatics and Computer Science: An International Journal
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 Representing and Generating Kernels by Fuzzy Equivalence Relations
The Journal of Machine Learning Research
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
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
Geometrical interpretation and applications of membership functions with fuzzy rough sets
Fuzzy Sets and Systems
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
An introduction to kernel-based learning algorithms
IEEE Transactions on Neural Networks
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Fuzzy similarity relations have been considered as kernels in the domain of machine learning in previous works. As a supplementary of this consideration, this paper focuses on construction of feature space related to fuzzy similarity relations as indefinite kernels. First we generalize the Mercer Theorem from positive definite kernels to fuzzy similarity relations. With this generalization we construct the feature space related to a fuzzy similarity relation as a particular Krein space. The proposed feature space is a naturally generalization of the existing Pseudo-Euclidean space from finite to infinite universe of discourses. At the end of this paper we develop an open problem to set up the connection between transitivity and the positive definiteness of a fuzzy similarity relation. Results in this paper complete the mathematical foundation for further applications of fuzzy similarity relations under the framework of kernel tricks.