# Kernels on fuzzy sets: an overview

## TL;DR

This paper provides an overview of kernels designed for fuzzy sets, defining various classes and discussing their applicability in machine learning and data science tasks involving uncertain data.

## Contribution

It introduces and categorizes kernels on fuzzy sets, expanding the toolkit for similarity measures in uncertain data contexts.

## Key findings

- Defined multiple classes of kernels on fuzzy sets
- Explored applicability in machine learning tasks
- Provided a theoretical framework for fuzzy set kernels

## Abstract

This paper introduces the concept of kernels on fuzzy sets as a similarity measure for $[0,1]$-valued functions, a.k.a. \emph{membership functions of fuzzy sets}. We defined the following classes of kernels: the cross product, the intersection, the non-singleton and the distance-based kernels on fuzzy sets. Applicability of those kernels are on machine learning and data science tasks where uncertainty in data has an ontic or epistemistic interpretation.