四种新的基于模糊β覆盖的粗糙集及其在三向逼近中的应用

IF 3.2 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2025-02-14 DOI:10.1016/j.fss.2025.109312

Haibo Jiang , Bao Qing Hu

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引用次数: 0

摘要

模糊粗糙集和三向决策作为不确定知识表示、学习和转换的有效方法，广泛应用于模糊概念的近似学习。基于模糊β覆盖的粗糙集作为模糊粗糙集的一种新的推广，可以灵活地表征不确定信息。然而，模糊β覆盖中一些概念存在不足，限制了其推广应用。一方面，模糊β-邻域和模糊β-共邻域不能保证它们具有自反性，这与具有自反性的脆邻域算子相反，存在语义理解困难。另一方面，大多数基于模糊β覆盖的粗糙集及其扩展模型不能满足β≠1时上近似包含下近似的性质，不能准确表征给定的客观概念。为了突破这些缺陷，我们首先提出了模糊β覆盖中的不可分辨模糊β邻域和不可分辨模糊β共邻域，这两种邻域都实现了自反性。然后，我们在模糊β覆盖近似空间中定义了四种新的基于模糊β覆盖的粗糙集，它们满足上下近似的包含关系。同时，还讨论了不同模型之间的一些基本性质和相互关系。进一步，我们给出了四种新的基于模糊β覆盖的粗糙集的拓扑性质。最后，我们给出了基于模糊β覆盖的粗糙集在模糊概念的三向逼近中的应用。将现有的基于模糊β覆盖的粗糙集模型与四种新模型进行了实验对比，结果表明了所提模型在近似学习方面的有效性和优越性。

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On four novel kinds of fuzzy β-covering-based rough sets and their applications to three-way approximations

Fuzzy rough sets and three-way decisions, as effective approaches for uncertain knowledge representation, learning and transformation, are widely used in approximate learning of fuzzy concepts. As a new generalization of fuzzy rough sets, fuzzy β-covering-based rough sets can characterize uncertain information flexibly. However, there exist shortcomings of some concepts in fuzzy β-covering, which limits its popularization and application. On the one side, fuzzy β-neighborhood and fuzzy β-co-neighborhood can not guarantee that they have the reflexivity property, which is contrary to the crisp neighborhood operators with reflexivity and has semantic difficulties in understanding. On the other side, most fuzzy β-covering-based rough sets and their extended models cannot satisfy the property that upper approximations contain lower approximations when

β \neq 1

, which can not characterize a given objective concept accurately. To break through these defects, we first propose an indiscernible fuzzy β-neighborhood and an indiscernible fuzzy β-co-neighborhood in fuzzy β-covering, both of which fulfill reflexivity. Then, we define four novel kinds of fuzzy β-covering-based rough sets in fuzzy β-covering approximation space, which satisfy the inclusion relationship of the upper and lower approximations. At the same time, some essential properties and the interrelationships between different models are also discussed. Furthermore, we give the topological properties of four novel kinds of fuzzy β-covering-based rough sets. Finally, we present an application of fuzzy β-covering-based rough sets to three-way approximations of fuzzy concepts. The comparative experimental results between the existing fuzzy β-covering-based rough set models and four novel models demonstrate the effectiveness and superiority of the proposed models in approximation learning.

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来源期刊

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.