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 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.