A revised and extended version of McShane-Whitney extensions for fuzzy Lipschitz maps

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

Fuzzy Sets and Systems Pub Date : 2026-04-15 Epub Date: 2025-12-17 DOI:10.1016/j.fss.2025.109731

Eduardo Jiménez-Fernández , Jesús Rodríguez-López , Aurora Sánchez-Martín-Orozco , Enrique A. Sánchez-Pérez

引用次数: 0

Abstract

In the paper [E. Jiménez-Fernández, J. Rodríguez-López, E. A. Sánchez-Pérez, Fuzzy Sets and Systems 406 (2021),66-81], a McShane-Whitney extension theorem is presented for real-valued fuzzy Lipschitz maps between fuzzy metric spaces. Specifically, the codomain space is considered as a so-called Euclidean fuzzy metric space

(R, M_{ϕ, g}, *) .

However, while the function ϕ is only required to be increasing, some results of the paper implicitly assume that ϕ is invertible, even though this is not explicitly stated. We propose here an alternative possibility that only requires ϕ to be also left-continuous.

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模糊Lipschitz地图的McShane-Whitney扩展的修订和扩展版本

在论文中[d]。Jiménez-Fernández， J. Rodríguez-López， E. a . Sánchez-Pérez, Fuzzy Sets and Systems 406(2021),66-81]，给出了模糊度量空间间实值模糊Lipschitz映射的McShane-Whitney扩展定理。具体来说，上域空间被认为是一个所谓的欧几里得模糊度量空间（R, m φ,g,*）。然而，虽然函数φ只需要增加，但本文的一些结果隐含地假设φ是可逆的，即使这没有明确说明。我们在这里提出了另一种可能性，只要求φ也是左连续的。

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.