On granular-ball fuzzy rough sets and applications in attribute evaluations

IF 3.2 1区 数学 Q2 COMPUTER SCIENCE, THEORY & METHODS
Anhui Tan , Danlu Feng , Jinjin Li , Wei-Zhi Wu
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引用次数: 0

Abstract

Granular-ball computing has emerged as a powerful framework for managing uncertainty, offering a more adaptive and interpretable approach to data analysis. In contrast, traditional fuzzy rough sets, which rely on fuzzy relations between individual data points, often suffer from limited granularity control, sensitivity to noise, and difficulties in handling large-scale or complex datasets. Moreover, the point-wise nature of fuzzy relations restricts the ability to capture group-based structural information inherent in real-world data. To address these limitations, we propose the granular-ball fuzzy rough set model, which integrates fuzzy rough set theory with the granular-ball computing paradigm. This novel model represents data in the form of fuzzy granular-balls, each encompassing a group of similar instances, thereby enhancing granularity management and improving robustness against noise and data sparsity. The lower and upper approximations in this model are redefined using these fuzzy granular-balls rather than individual objects, with the purity of each granular-ball directly influencing the certainty and precision of classification boundaries. This approach facilitates smoother and more stable delineations of positive, negative, and boundary regions in uncertain classification tasks. Additionally, the model introduces monotonous fuzzy granular-ball partitions that evolve with expanding attribute sets, providing a practical mechanism for evaluating attribute significance in feature selection. Overall, the proposed model retains the mathematical rigor of traditional fuzzy rough set theory while offering enhanced flexibility, interpretability, and effectiveness in handling real-world uncertain data.
颗粒球模糊粗糙集及其在属性评价中的应用
颗粒球计算已经成为一种管理不确定性的强大框架,为数据分析提供了一种更具适应性和可解释性的方法。相比之下,传统的模糊粗糙集依赖于单个数据点之间的模糊关系,往往存在粒度控制有限、对噪声敏感、难以处理大规模或复杂数据集的问题。此外,模糊关系的逐点性质限制了捕捉真实数据中固有的基于组的结构信息的能力。为了解决这些限制,我们提出了颗粒球模糊粗糙集模型,该模型将模糊粗糙集理论与颗粒球计算范式相结合。这种新模型以模糊颗粒球的形式表示数据,每个颗粒球包含一组相似的实例,从而增强粒度管理,提高抗噪声和数据稀疏性的鲁棒性。该模型使用这些模糊颗粒球而不是单个对象来重新定义上下近似,每个颗粒球的纯度直接影响分类边界的确定性和精度。这种方法有助于在不确定分类任务中更平滑、更稳定地描绘正、负和边界区域。此外,该模型引入了单调的模糊颗粒球划分,随着属性集的扩展而演化,为特征选择中的属性重要性评估提供了一种实用的机制。总的来说,提出的模型保留了传统模糊粗糙集理论的数学严谨性,同时在处理现实世界的不确定数据时提供了增强的灵活性、可解释性和有效性。
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来源期刊
Fuzzy Sets and Systems
Fuzzy Sets and Systems 数学-计算机:理论方法
CiteScore
6.50
自引率
17.90%
发文量
321
审稿时长
6.1 months
期刊介绍: Since its launching in 1978, the journal Fuzzy Sets and Systems has been devoted to the international advancement of the theory and application of fuzzy sets and systems. The theory of fuzzy sets now encompasses a well organized corpus of basic notions including (and not restricted to) aggregation operations, a generalized theory of relations, specific measures of information content, a calculus of fuzzy numbers. Fuzzy sets are also the cornerstone of a non-additive uncertainty theory, namely possibility theory, and of a versatile tool for both linguistic and numerical modeling: fuzzy rule-based systems. Numerous works now combine fuzzy concepts with other scientific disciplines as well as modern technologies. In mathematics fuzzy sets have triggered new research topics in connection with category theory, topology, algebra, analysis. Fuzzy sets are also part of a recent trend in the study of generalized measures and integrals, and are combined with statistical methods. Furthermore, fuzzy sets have strong logical underpinnings in the tradition of many-valued logics.
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