More on decompositions of a fuzzy set in fuzzy topological spaces
type: Item
instance of: scholarly article
zbMATH Open document ID: 1372.54008
author: H. Maki
author: Sayaka Hamada
publication date: 2016-06-29T00:00:00Z
full work available at URL: abst2015-1.pdf
full work available at URL: 2015-1.pdf
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 03E72
zbMATH DE Number: 6599617
zbMATH Keywords: Chang's fuzzy topology
zbMATH Keywords: fuzzy point
zbMATH Keywords: decompositions of fuzzy sets
zbMATH Keywords: the digital \(n\)-space
MaRDI profile type: Publication
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title: More on decompositions of a fuzzy set in fuzzy topological spaces
published in: Scientiae Mathematicae Japonicae
review text: Autors' abstract: Using new properties of the concept of fuzzy points in the sense of Pu Pao-Ming and Liu Ying-Ming, we first prove that every fuzzy set \(\lambda\not=0\) is decomposed by two fuzzy sets \(\lambda_{\mathcal{O}(X,\sigma^f)}\) and \(\lambda^\ast_{\mathcal{PC}(X,\sigma^f )}\), where \((X,\sigma^f)\) is a specified Chang's fuzzy space. Namely, \(\lambda = \lambda_{\mathcal{O}(X,\sigma^f )}\vee \lambda^\ast_{\mathcal{PC}(X,\sigma^f )}\) and \(\lambda_{\mathcal{O}(X,\sigma^f )}\wedge \lambda^\ast_{\mathcal{PC}(X,\sigma^f )}=0\) hold, and the fuzzy set \(\lambda_{\mathcal{O}(X,\sigma^f)}\) is fuzzy open in \((X,\sigma^f)\). Finally, these results are applied to the case where \(X =\mathbb{Z}^n (n > 0)\) and \(\sigma^f = (\kappa^n)^f\), where the topological space \((X, \sigma)\) is the digital \(n\)-space \((\mathbb{Z}^n, \kappa^n)\).
reviewed by: Fu-Gui Shi
description: scientific article; zbMATH DE number 6599617