On fuzzy convergence
type: Item
instance of: scholarly article
title: On fuzzy convergence
zbMATH Open document ID: 0614.54008
DOI: 10.1016/0020-0255(86)90040-X
author: Giangiacomo Gerla
published in: Information Sciences
publication date: 1986-01-01T00:00:00Z
review text: First, summarizing his paper ''On the concept of fuzzy point'' [Fuzzy Sets Syst. 18, 159-172 (1986; Zbl 0606.03014)], the author shows that a ''good definition of fuzzy point'' is impossible if one wants \(\in\) to be a nonfuzzy relation between fuzzy points and fuzzy subsets. Instead, he admits that points and sets are nonfuzzy objects while \(\in\) is a fuzzy relation. So, interpreting in a multivalued logic the concepts of subsets, point, topology and two different formulas expressing the classical convergence, he obtains concepts of convergence for sequences of elements of a set w.r.t. a fuzzy topology. Finally, he investigates convergences preserving operators in functional spaces and the uniqueness of limits.
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 54A20
Mathematics Subject Classification ID: 03E72
Mathematics Subject Classification ID: 03B50
Mathematics Subject Classification ID: 03B52
zbMATH DE Number: 3994511
zbMATH Keywords: membership relation
zbMATH Keywords: multivalued first order logic
zbMATH Keywords: fuzzy convergence
zbMATH Keywords: Zadeh space
zbMATH Keywords: L-fuzzy topology
zbMATH Keywords: fuzzy point
zbMATH Keywords: fuzzy relation
zbMATH Keywords: convergences preserving operators
reviewed by: Bernhard Behrens
MaRDI profile type: Publication
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description: scientific article; zbMATH DE number 3994511