Notes on anti \(L\)-fuzzy subfield of a field
type: Item
instance of: scholarly article
zbMATH Open document ID: 1293.12006
publication date: 2013-10-30T00:00:00Z
full work available at URL: index.html
Mathematics Subject Classification ID: 12F99
Mathematics Subject Classification ID: 08A72
zbMATH DE Number: 6220902
zbMATH Keywords: \(L\)-fuzzy set
zbMATH Keywords: anti \(L\)-fuzzy subfield
MaRDI profile type: Publication
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author: M. Vasu
author: D. Sivakumar
title: Notes on anti \(L\)-fuzzy subfield of a field
published in: International Journal of Algebra
review text: Let \((F,+,.)\) be a field. An L-fuzzy subset \(A\) of \(F\) is said to be an anti-L-fuzzy subfield of \(F\) if the following conditions are satisfied: {\parindent=6mm \begin{itemize}\item[(1)] \(A(x + y) \leq A(x) \vee A(y)\), for all \(x, y \in F\), \item[(2)] \(A(-x) \leq A(x)\), for all \(x \in F\), \item[(3)] \(A(x . y) \leq A(x) \vee A(y)\), for all \(x, y \in F\), \item[(4)] \(A(x^{-1}) \leq A(x)\), for all \(x \in F - \{ 0 \}\), where 0 is the additive identity element of \(F\). NEWLINENEWLINE\end{itemize}} Some properties of the anti-L-fuzzy subfield are discussed.
reviewed by: Krassimir Atanassov
description: scientific article; zbMATH DE number 6220902