The theory of global fuzzy neighborhood structures. I: The general case
type: Item
instance of: scholarly article
title: The theory of global fuzzy neighborhood structures. I: The general case
zbMATH Open document ID: 0934.54004
DOI: 10.1016/S0165-0114(97)00111-5
author: Werner Gähler
author: Fatma Bayoumi
author: A. Kandil
author: Ali Ahmed Nouh
published in: Fuzzy Sets and Systems
publication date: 2000-04-10T00:00:00Z
review text: The first named author [ibid. 76, No. 2, 205-224, 225-246 (1995; Zbl 0873.54008; Zbl 0873.54009)] characterized fuzzy topologies (stratified fuzzy topologies) as monadic topologies with respect to the partially ordered fuzzy filter monad (homogeneous fuzzy filter monad, respectively). Weakening certain conditions in the definition of monadic topologies, the authors in this paper introduce the concept of global fuzzy neighbourhood structures, which was proved to contain fuzzy topologies and etc. as special cases. Three kinds of global fuzzy neighbourhood structures, corresponding to three kinds of fuzzy filters, are studied systematically; particularly their relationship to fuzzy topologies, stratified fuzzy topologies and the fuzzy neighbourhood space topologies in the sense of \textit{R. Lowen} [ibid. 7, 165-189 (1982; Zbl 0487.54008)] are investigated.
reviewed by: Dexue Zhang
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54B30
zbMATH DE Number: 1320350
zbMATH Keywords: fuzzy filter monad
zbMATH Keywords: monadic topologies
MaRDI profile type: Publication
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full work available at URL: s0165-0114(97)00111-5
OpenAlex ID: W2093664908
description: scientific article; zbMATH DE number 1320350