Fréchet fuzzy metric
type: Item
instance of: scholarly article
title: Fréchet fuzzy metric
zbMATH Open document ID: 1501.54006
author: O. Berezsky
author: Lidiya Bazylevych
author: Mykhailo Zarichnyi
published in: Matematychni Studiï
publication date: 2022-10-20T00:00:00Z
review text: The paper deals with the Fréchet distance in a fuzzy metric space in the sense of George and Veeramani. The fuzzy distance between the curves \(\gamma_1, \gamma_2\) is defined as \(M_F (\gamma_1, \gamma_2, t) = \sup \inf M(\gamma_1(\alpha(s)), \gamma_2(s), t)\), where the inf is taken over all \(s\) in the unit interval and the sup is taken over all the homeomorphisms \(\alpha\) of the unit interval. It is shown that \(M_F\) is a metric on the set of all continuous mappings on the universe. Similar results are shown also for the fuzzy metric \(M'(x,y,t) = e^{-\frac{d(x,y)}{t^n}}, n \in N\). A non-monotonic version of the Fréchet distance is considered as well.
reviewed by: Vladimír Janiš
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B20
Mathematics Subject Classification ID: 54E35
zbMATH DE Number: 7604460
zbMATH Keywords: metric spaces
zbMATH Keywords: fuzzy metric
zbMATH Keywords: Fréchet distance
MaRDI profile type: Publication
full work available at URL: ms.57.2.210-215
OpenAlex ID: W4293058239
DOI: 10.30970/MS.57.2.210-215
description: scientific article; zbMATH DE number 7604460