Fuzzy equality and convergences for F-observables in F-quantum spaces
type: Item
instance of: scholarly article
title: Fuzzy equality and convergences for F-observables in F-quantum spaces
zbMATH Open document ID: 0732.28010
author: Ferdinand Chovanec
author: František Kôpka
published in: Applications of Mathematics
publication date: 1991-01-01T00:00:00Z
full work available at URL: https://eudml.org/doc/15658
review text: The paper deals with F-states (P-measures) and F-observables on F-quantum spaces (soft fuzzy \(\sigma\)-algebras). Fuzzy equalities and fuzzy inequalities are defined for fuzzy sets, F-observables and the corresponding notions in the representation of \textit{A. Dvurečenskij} [On a representation of observables in fuzzy measurable spaces, to appear in J. Math. Anal. Appl.]. The authors introduce 14 types of convergence of F-observables. These appear to be equivalent to the corresponding types of convergence of measurable functions on a Boolean \(\sigma\)- algebra used in the representation. Using this fact, a series of implications between various types of convergence is proved.
Mathematics Subject Classification ID: 28E10
Mathematics Subject Classification ID: 28A20
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 4210475
zbMATH Keywords: convergence of observables
zbMATH Keywords: F-states
zbMATH Keywords: P-measures) and F-observables on F- quantum spaces
zbMATH Keywords: soft fuzzy \(\sigma \) -algebras
zbMATH Keywords: Fuzzy equalities
zbMATH Keywords: fuzzy inequalities
zbMATH Keywords: fuzzy sets
reviewed by: Mirko Navara
MaRDI profile type: Publication
cites work: Measure theoretic convergences of observables and operators
cites work: On the existence of probability measures on fuzzy measurable spaces
cites work: Probability of fuzzy events defined as denumerable additivity measure
cites work: Q3812249
cites work: On a representation of observables in fuzzy measurable spaces
cites work: On joint distribution of observables for \(F\)-quantum spaces
OpenAlex ID: W3047718051
DOI: 10.21136/AM.1991.104442
description: scientific article; zbMATH DE number 4210475