Fuzzy Rough Sets Based on Fuzzy Quantification

TL;DR

This paper introduces fuzzy quantifier-based fuzzy rough sets (FQFRS), improving noise sensitivity issues in classical fuzzy rough sets by generalizing with unary and binary quantification models, and demonstrates their effectiveness in classification tasks.

Contribution

The paper proposes FQFRS, a novel generalization of fuzzy rough sets using fuzzy quantifiers, addressing limitations of VQFRS and enhancing performance in machine learning applications.

Findings

FQFRS generalizes existing models including VQFRS and OWAFRS.

Yager's Weighted Implication-based (YWI) model improves classification performance.

FQFRS models show theoretical robustness and practical effectiveness in experiments.

Abstract

One of the weaknesses of classical (fuzzy) rough sets is their sensitivity to noise, which is particularly undesirable for machine learning applications. One approach to solve this issue is by making use of fuzzy quantifiers, as done by the vaguely quantified fuzzy rough set (VQFRS) model. While this idea is intuitive, the VQFRS model suffers from both theoretical flaws as well as from suboptimal performance in applications. In this paper, we improve on VQFRS by introducing fuzzy quantifier-based fuzzy rough sets (FQFRS), an intuitive generalization of fuzzy rough sets that makes use of general unary and binary quantification models. We show how several existing models fit in this generalization as well as how it inspires novel ones. Several binary quantification models are proposed to be used with FQFRS. We conduct a theoretical study of their properties, and investigate their potential by applying them to classification problems. In particular, we highlight Yager's Weighted Implication-based (YWI) binary quantification model, which induces a fuzzy rough set model that is both a significant improvement on VQFRS, as well as a worthy competitor to the popular ordered weighted averaging based fuzzy rough set (OWAFRS) model.