Fuzzy cores and their extensions
type: Item
instance of: scholarly article
title: Fuzzy cores and their extensions
zbMATH Open document ID: 0794.54010
DOI: 10.1016/0165-0114(93)90122-X
author: Nehad N. Morsi
published in: Fuzzy Sets and Systems
publication date: 1994-09-04T00:00:00Z
review text: A fuzzy core on a carrier set \(X\) is defined as an operator on a subfamily of \([0,1]^ X\) into \([0,1]^ X\) subject to conditions motivated by the definition of a Čech closure. The author notes that fuzzy Čech and Kuratowski operators induce fuzzy cores and examines several ways of extending a core operator to all fuzzy subsets of the carrier. These extensions lead to six notions of continuity for maps between fuzzy cores, and interconnections among them are established. Lastly, the author shows that the Scott topology, Klein's generating families of \(\alpha\)-closure operators, and Mashhour's pseudo-closure operators can be obtained from fuzzy cores.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 496204
zbMATH Keywords: Čech closure
zbMATH Keywords: Scott topology
MaRDI profile type: Publication
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full work available at URL: 0165-0114(93)90122-x
OpenAlex ID: W1963525072
description: scientific article; zbMATH DE number 496204