论文标题
基于模糊量化的模糊粗糙集
Fuzzy Rough Sets Based on Fuzzy Quantification
论文作者
论文摘要
古典（模糊）粗糙集的弱点之一是它们对噪声的敏感性，这对于机器学习应用尤其不可能。解决此问题的一种方法是使用模糊的量词，这是由模糊量化的模糊集合（VQFRS）模型所做的。尽管这个想法是直观的，但VQFRS模型均遭受理论缺陷以及应用程序中最佳性能的损害。在本文中，我们通过引入基于模糊量化的模糊粗糙集（FQFRS）来改进VQFR，这是对模糊粗糙集的直观概括，可利用一般的一般性和二进制量化模型。我们展示了几种现有模型如何适合这种概括以及它如何启发新颖的模型。建议将几种二进制定量模型与FQFR一起使用。我们对其特性进行了理论研究，并通过将它们应用于分类问题来研究其潜力。特别是，我们重点介绍了Yager的基于加权影响的（YWI）二进制量化模型，该模型诱发了模糊的粗糙集模型，既可以对VQFR进行重大改进，也是值得的竞争对手，对受欢迎的有序加权平均基于平均的模糊模糊粗糙集（OWAFRS）模型。
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.
