Lattice-valued coarse structures

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

Fuzzy Sets and Systems Pub Date : 2024-11-04 DOI:10.1016/j.fss.2024.109175

Yongchao Wang , Bin Pang , Fu-Gui Shi

引用次数: 0

Abstract

Based on a complete residuated lattice L, we propose a new approach to fuzzification of coarse structures. Firstly, we introduce the concepts of L-entourages and L-(quasi, semi)-coarse structures and study the maps between L-coarse spaces. Secondly, we provide some examples of L-coarse structures from the aspects of L-metrics, L-relations and L-hyperstructures. Thirdly, we introduce the notion of L-ball structures to characterize L-coarse structures. Finally, we establish the relationship among L-entourage spaces, L-quasi-coarse spaces, L-semi-coarse spaces and L-coarse spaces in a categorical viewpoint.

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格值粗结构

基于完整的残差网格 L，我们提出了一种模糊化粗结构的新方法。首先，我们介绍了 L-梯度和 L-（准、半）粗结构的概念，并研究了 L-粗空间之间的映射。其次，我们从 L-度量、L-关系和 L-超结构等方面提供了一些 L-粗结构的例子。第三，我们引入 L 球结构的概念来表征 L 粗结构。最后，我们从分类的角度建立了 L-鼓励空间、L-准粗大空间、L-半粗大空间和 L-粗大空间之间的关系。

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.