The extension theorem of F-measure spaces
type: Item
instance of: scholarly article
title: The extension theorem of F-measure spaces
zbMATH Open document ID: 0543.28003
DOI: 10.1016/S0165-0114(83)80067-0
author: Daopeng Zheng
published in: Fuzzy Sets and Systems
publication date: 1983-01-01T00:00:00Z
review text: A fuzzy \(\sigma\)-algebra of fuzzy subsets is a special \(\sigma\)-complete, distributive lattice equipped with an order reversing involution, and a fuzzy measure is a positive \(\sigma\)-continuous valuation on a given fuzzy \(\sigma\)-algebra. The author proves two different extension theorems: The first theorem is a generalization of the Caratheodory extension of ordinary masure spaces to fuzzy measure spaces, the second one is an extension theorem of fuzzy measures from a fuzzy \(\sigma\)- algebra \({\mathcal A}\) to the normal extension of \({\mathcal A}\) which uses in a crucial way a representation theorem of fuzzy probability measures due to \textit{E. P. Klement, R. Lowen} and \textit{W. Schwyhla} [cf. Fuzzy Sets Syst. 5, 21-30 (1981; Zbl 0447.28005)].
Mathematics Subject Classification ID: 28A10
Mathematics Subject Classification ID: 28A99
zbMATH DE Number: 3863525
zbMATH Keywords: outer measures of fuzzy subsets
zbMATH Keywords: fuzzy \(\sigma\)-algebra of fuzzy subsets
zbMATH Keywords: fuzzy measure
zbMATH Keywords: extension theorems
zbMATH Keywords: Caratheodory extension
zbMATH Keywords: fuzzy probability measures
MaRDI profile type: Publication
full work available at URL: s0165-0114(83)80067-0
OpenAlex ID: W1972723563
description: scientific article; zbMATH DE number 3863525