Tight spans of fuzzy metric spaces

IF 3.1 1区数学 Q2 COMPUTER SCIENCE, THEORY & METHODS

Fuzzy Sets and Systems Pub Date : 2026-03-15 Epub Date: 2025-11-22 DOI:10.1016/j.fss.2025.109700

Yi Shi , Hui Yang

引用次数: 0

Abstract

Dress in 1984 introduced the concept of tight span of a metric space, allowing the space to be isometrically embedded into a larger metric space. This paper aims to extend this theory to fuzzy metric setting. More concretely, we define tight spans of fuzzy metric spaces as a key tool in the study of the appropriate extension. It is shown that any fuzzy metric space can be isometrically embedded into its tight span, with the embedding being an isomorphism when the fuzzy metric space is hyperconvex (or, equivalently, injective). Additionally, we explore tight extensions and essential extensions of fuzzy metric spaces, providing a precise formulation of their hyperconvex hulls and injective hulls.

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模糊度量空间的紧跨度

Dress在1984年引入了一个公制空间的紧密跨度概念，使得空间可以等距嵌入到一个更大的公制空间中。本文旨在将这一理论推广到模糊度量集。更具体地说，我们定义模糊度量空间的紧跨度作为研究适当扩展的关键工具。证明了任何模糊度量空间都可以等距嵌入到它的紧跨中，当模糊度量空间是超凸的（或等价地，内射的）时，嵌入是同构的。此外，我们探讨了模糊度量空间的紧扩展和本质扩展，提供了它们的超凸包和注入包的精确公式。

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.