Fuzzy-System Kernel Machines: A Kernel Method Based on the Connections Between Fuzzy Inference Systems and Kernel Machines

This article introduces the fuzzy-system kernel machines -a class of machine learning models based on the connection between fuzzy inference systems and kernel machines. For the connection, we observed a relationship between the representer theorem of kernel methods and the functional representation...

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Bibliographic Details
Published in:IEEE transactions on fuzzy systems 2022-10, Vol.30 (10), p.4447-4459
Main Authors: Guevara, Jorge, Mendel, Jerry M., Hirata, Roberto
Format: Article
Language:English
Subjects:
Fuzzy logic
Fuzzy sets
Fuzzy systems
Inference
Kernel
Kernel functions
kernel machines
Machine learning
Machine learning algorithms
Symmetric matrices
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Summary:This article introduces the fuzzy-system kernel machines -a class of machine learning models based on the connection between fuzzy inference systems and kernel machines. For the connection, we observed a relationship between the representer theorem of kernel methods and the functional representation of nonsingleton fuzzy systems. We found that the nonsingleton kernel on fuzzy sets -a kernel defined in this article-is the core element allowing this two-way connection perspective. Consequently, a fuzzy system trained with the kernel method can be regarded as a kernel machine, whereas a kernel machine trained with a nonsingleton kernel on fuzzy sets can be interpreted as a fuzzy system. We conducted several experiments in supervised classification to understand the generalization power and properties of the proposed fuzzy-system kernel machines.
ISSN:1063-6706
1941-0034
DOI:10.1109/TFUZZ.2022.3153141