Fuzzy Sets and Systems
Nonlinear component analysis as a kernel eigenvalue problem
Neural Computation
Menger and Ovchinnikovs on indistinguishabilities, revisited
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems - Special issue on selected papers on fuzzy logic and fuzzy technology from ESTYLF '98
Foundations of Fuzzy Systems
Domination of aggregation operators and preservation of transitivity
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
A note on approximate equality versus the Poincaré paradox
Fuzzy Sets and Systems - Theme: Basic notions
On many-valued partitions and many-valued equivalence relations
International Journal of Uncertainty, Fuzziness and Knowledge-Based Systems
Classes of kernels for machine learning: a statistics perspective
The Journal of Machine Learning Research
Kernel Based Algorithms for Mining Huge Data Sets: Supervised, Semi-supervised, and Unsupervised Learning (Studies in Computational Intelligence)
RSKT '09 Proceedings of the 4th International Conference on Rough Sets and Knowledge Technology
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
Feature Selection via Maximizing Fuzzy Dependency
Fundamenta Informaticae
Geometrical interpretation and applications of membership functions with fuzzy rough sets
Fuzzy Sets and Systems
Parameterized attribute reduction with Gaussian kernel based fuzzy rough sets
Information Sciences: an International Journal
Fuzzy relational equations with min-biimplication composition
Fuzzy Optimization and Decision Making
Statistically---Induced kernel function for support vector machine classifier
ICAISC'12 Proceedings of the 11th international conference on Artificial Intelligence and Soft Computing - Volume Part I
Kernelized Fuzzy Rough Sets Based Yawn Detection for Driver Fatigue Monitoring
Fundamenta Informaticae - Knowledge Technology
The quest for transitivity, a showcase of fuzzy relational calculus
WCCI'12 Proceedings of the 2012 World Congress conference on Advances in Computational Intelligence
Fast window fusion using fuzzy equivalence relation
Pattern Recognition Letters
Structure of feature spaces related to fuzzy similarity relations as kernels
Fuzzy Sets and Systems
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Kernels are two-placed functions that can be interpreted as inner products in some Hilbert space. It is this property which makes kernels predestinated to carry linear models of learning, optimization or classification strategies over to non-linear variants. Following this idea, various kernel-based methods like support vector machines or kernel principal component analysis have been conceived which prove to be successful for machine learning, data mining and computer vision applications. When applying a kernel-based method a central question is the choice and the design of the kernel function. This paper provides a novel view on kernels based on fuzzy-logical concepts which allows to incorporate prior knowledge in the design process. It is demonstrated that kernels mapping to the unit interval with constant one in its diagonal can be represented by a commonly used fuzzy-logical formula for representing fuzzy rule bases. This means that a great class of kernels can be represented by fuzzy-logical concepts. Apart from this result, which only guarantees the existence of such a representation, constructive examples are presented and the relation to unlabeled learning is pointed out.