On the boundary of fuzzy sets
type: Item
instance of: scholarly article
title: On the boundary of fuzzy sets
zbMATH Open document ID: 0926.54001
DOI: 10.1016/S0165-0114(96)00084-X
author: Juan Tarrés
author: Eduardo Cuchillo-Ibáñez
published in: Fuzzy Sets and Systems
publication date: 1999-02-17T00:00:00Z
review text: A new concept of boundary (here called frontier) \(\text{Fr} (\mu)\) of a fuzzy set \(\mu\) in a fuzzy topological space \(X\) is given. The properties of the frontier are studied. Some of the results are as follows. A fuzzy set \(\mu\) in \(X\) is clopen iff \(\text{Fr }\mu= 0_X\); \(\mu\) is not clopen iff \(\text{Fr }\mu\) and \(\text{Fr} (1_X-\mu)\) are overlapping fuzzy sets. If \(\mu\) is a closed fuzzy set of \(X\), then \(\text{Fr }\mu= \text{Fr Fr }\mu\). If \(Y\) is a fuzzy subspace of \(X\) and \(\mu\) is a fuzzy set in \(X\) then \(\text{Fr} (\mu|_Y)\leq \text{Fr } \mu|_Y\) holds.
Mathematics Subject Classification ID: 54A40
zbMATH DE Number: 1251627
zbMATH Keywords: frontier
reviewed by: Dušan Adnadjević
MaRDI profile type: Publication
cites work: Dimension of fuzzy spaces
cites work: Some properties of the dimension F-Ind of GF-spaces
cites work: Fuzzy topological spaces
cites work: Fuzzy topological spaces and fuzzy compactness
cites work: Q4095531
cites work: Fuzzy sets
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description: scientific article; zbMATH DE number 1251627