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.

Fuzzy quantification is a subtopic of fuzzy logic which deals with the modelling of the quantified expressions we can find in natural language. Fuzzy quantifiers have been successfully applied in several fields like fuzzy, control, fuzzy databases, information retrieval, natural language generation, etc. Their ability to model and evaluate linguistic expressions in a mathematical way, makes fuzzy quantifiers very powerful for data analytics and data mining applications. In this paper we will give a general overview of the main applications of fuzzy quantifiers in this field as well as some ideas to use them in new application contexts.

Important advances have been made in the fuzzy quantification field. Nevertheless, some problems remain when we face the decision of selecting the most convenient model for a specific application. In the literature, several desirable adequacy properties have been proposed, but theoretical limits impede quantification models from simultaneously fulfilling every adequacy property that has been defined. Besides, the complexity of model definitions and adequacy properties makes very difficult for real users to understand the particularities of the different models that have been presented. In this work we will present several criteria conceived to help in the process of selecting the most adequate Quantifier Fuzzification Mechanisms for specific practical applications. In addition, some of the best known well-behaved models will be compared against this list of criteria. Based on this analysis, some guidance to choose fuzzy quantification models for practical applications will be provided.