Some properties of fuzzy integrable function space \(L^ 1(\mu)\)
type: Item
instance of: scholarly article
title: Some properties of fuzzy integrable function space \(L^ 1(\mu)\)
zbMATH Open document ID: 0693.46026
DOI: 10.1016/0165-0114(89)90209-1
author: Congxin Wu
author: Ming Ma
published in: Fuzzy Sets and Systems
publication date: 1989-01-01T00:00:00Z
review text: A measurable space (X,\(\mu)\) with fuzzy measure \(\mu\) is considered [see \textit{M. Sugeno}, Theory of fuzzy integrals and its applications, Thesis, Tokyo Institute of Technology (1974)]. Fuzzy Orlicz class \(L_{\Phi}(\mu)\) and fuzzy \(\Phi\)-mean convergence are introduced and it is proved, that for every Orlicz function \(\Phi\) the space \(L_{\Phi}(\mu)\) is equal to the space \(L^ 1(\mu)\)- defined as \(L_{\Phi}(\mu)\) whenever \(\Phi (x)=x\). It is proved that convergence in fuzzy measure in the space S(\(\mu)\) of all \(\mu\)-measurable functions coincides with fuzzy \(\Phi\)-mean convergence for any Orlicz function \(\Phi\). Also necessary and sufficient conditions for equality \(L^ 1(\mu)=S(\mu)\) are given.
Mathematics Subject Classification ID: 46E30
Mathematics Subject Classification ID: 28E10
zbMATH DE Number: 4134819
zbMATH Keywords: fuzzy integrable function
zbMATH Keywords: Fuzzy Orlicz class
zbMATH Keywords: fuzzy \(\Phi\)-mean convergence
zbMATH Keywords: convergence in fuzzy measure
reviewed by: Fedor Sukochev
MaRDI profile type: Publication
full work available at URL: 0165-0114(89)90209-1
OpenAlex ID: W2063439545
cites work: Toward a general theory of fuzzy variables
cites work: The fuzzy integral
cites work: Q4077278
description: scientific article; zbMATH DE number 4134819