On the lattice of fuzzy rough sets

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

Fuzzy Sets and Systems Pub Date : 2024-05-08 DOI:10.1016/j.fss.2024.108999

Dávid Gégény , Sándor Radeleczki

引用次数: 0

Abstract

By the means of lower and upper fuzzy approximations we define quasiorders. Their properties are used to prove our main results. First, we characterize the pairs of fuzzy sets that form fuzzy rough sets w.r.t. a t-similarity relation θ on U, for certain t-norms and implicators. If U is finite or the range of θ and of the fuzzy sets is a fixed finite chain, we establish conditions under which fuzzy rough sets form lattices. We show that this is the case for the min t-norm and any S-implicator defined by an involutive negator and the max co-norm.

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关于模糊粗糙集网格

通过下模糊近似和上模糊近似，我们定义了准绳。我们利用它们的特性来证明我们的主要结果。首先，我们描述了在一定的 t 准则和蕴涵器下，与 U 上的 t 相似关系 θ 形成模糊粗糙集的模糊集对的特征。如果 U 是有限的，或者 θ 和模糊集的范围是一个固定的有限链，我们就建立了模糊粗糙集形成网格的条件。我们证明了最小 t-norm 和任何由非卷积否定式和最大协norm 定义的 S- 隐含子都是这种情况。

本文章由计算机程序翻译，如有差异，请以英文原文为准。

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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.