Fuzzy vector spaces under triangular norms
type: Item
instance of: scholarly article
title: Fuzzy vector spaces under triangular norms
zbMATH Open document ID: 0631.54003
DOI: 10.1016/0165-0114(88)90101-7
author: Phullendu Das
published in: Fuzzy Sets and Systems
publication date: 1988-01-01T00:00:00Z
review text: Let E be a vector space over a field K and F a fuzzy set defined on E. According to \textit{A. K. Katsaras} and \textit{D. B. Liu} [J. Math. Anal. Appl. 58, 135-146 (1977; Zbl 0358.46011)] F is a fuzzy subspace of E if \(F(x+y)\leq \min (F(x),F(y))\) and F(kx)\(\geq F(x)\) for all x,y\(\in E\) and \(k\in K\). In this paper the author uses a t-norm instead of minimum. Many theorems obtained are generalizations of the corresonding results by Katsaras and Liu. However, this generalization of a fuzzy subspace was introduced earlier by \textit{Yu Yandong} [Fuzzy Math. 4, No.2, 29-40 (1984; Zbl 0565.46008) and ibid. No.3, 59-62 (1984; Zbl 0565.46009)]. These papers also contain several elementary theorems, which are proved here.
reviewed by: Osmo Kaleva
Mathematics Subject Classification ID: 54A40
Mathematics Subject Classification ID: 46A99
zbMATH DE Number: 4026315
zbMATH Keywords: T-convex fuzzy set
zbMATH Keywords: t-norm
zbMATH Keywords: fuzzy subspace
MaRDI profile type: Publication
full work available at URL: 0165-0114(88)90101-7
OpenAlex ID: W2043511449
cites work: Fuzzy groups redefined
cites work: A characterization of fuzzy subgroups
cites work: Fuzzy vector spaces and fuzzy topological vector spaces
cites work: Fuzzy invariant subgroups and fuzzy ideals
cites work: On the direct product of fuzzy subgroups
cites work: Fuzzy groups
cites work: Statistical metric spaces
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cites work: Fuzzy groups and level subgroups
cites work: Fuzzy sets
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description: scientific article; zbMATH DE number 4026315