Rough set theory is a well-known mathematical framework that can deal with
inconsistent data by providing lower and upper approximations of concepts. A
prominent property of these approximations is their granular representation:
that is, they can be written as unions of simple sets, called granules. The
latter can be identified with "if. . . , then. . . " rules, which form the
backbone of rough set rule induction. It has been shown previously that this
property can be maintained for various fuzzy rough set models, including those
based on ordered weighted average (OWA) operators. In this paper, we will focus
on some instances of the general class of fuzzy quantifier-based fuzzy rough
sets (FQFRS). In these models, the lower and upper approximations are evaluated
using binary and unary fuzzy quantifiers, respectively. One of the main targets
of this study is to examine the granular representation of different models of
FQFRS. The main findings reveal that Choquet-based fuzzy rough sets can be
represented granularly under the same conditions as OWA-based fuzzy rough sets,
whereas Sugeno-based FRS can always be represented granularly. This observation
highlights the potential of these models for resolving data inconsistencies and
managing noise.

粗糙集理论是一个可以通过提供概念下限和上限的近似来处理不一致数据的著名数学框架。本研究关注于模糊量词型模糊粗集的领域，并发现了广义 FQFRS 模型的粒状表示，强调了这些模型在解决数据不一致性和管理噪音方面的潜力。

关于模糊量词模糊粗糙集的颗粒表示

On the Granular Representation of Fuzzy Quantifier-Based Fuzzy Rough  Sets

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.

本文改进了模糊量化模糊粗糙集（VQFRS）模型，引入了基于模糊量词的模糊粗糙集（FQFRS）模型，使用泛化的一元和二元量化模型，并应用多个二元量化模型来分类，特别地，介绍了 Yager 的基于加权蕴涵的二元量化模型在 FQFRS 中的优化作用。