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

Abstract

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.