Fuzzy rough sets based on fuzzy quantification

Classical (fuzzy) rough sets exhibit 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), which proposes an intuitive fuzzy rough approximation operator that utilizes general unary and binary quantification models. We show how several existing models fit inside FQFRS, as well as how it inspires novel ones. Additionally, we propose several binary quantification models to be used with FQFRS. Furthermore, we conduct a theoretical study of their properties, and investigate their potential by applying them to classification problems. In particular, we highlight the effectiveness of 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.