Fuzzy prime ideals and invertible fuzzy ideals in BCK-algebras
type: Item
instance of: scholarly article
title: Fuzzy prime ideals and invertible fuzzy ideals in BCK-algebras
zbMATH Open document ID: 0968.06014
DOI: 10.1016/S0165-0114(98)00428-X
author: Xiaolong Xin
author: Young Bae Jun
published in: Fuzzy Sets and Systems
publication date: 2001-09-12T00:00:00Z
review text: Let \(\mu\) and \(\nu\) be fuzzy ideals of a commutative BCK-algebra \(X\). \(\mu\) is called prime iff it is non-constant and \(\mu(x\wedge y)=\max\{\mu(x), \mu(y)\}\) for all \(x,y\in X\). If \(\nu^+ (x)=1-\inf\{\nu(y) |y\wedge x=0\}\) is a fuzzy ideal of \(X\), then \(\nu\) is called invertible. Every fuzzy prime ideal is invertible, but not conversely. If all fuzzy ideals of a bounded implicative BCK-algebra \(X\) are invertible, then for all fuzzy prime ideals \(\mu\), \(\nu\), the ideals \(\mu\cup\nu\) and \(\mu\cap\nu\) are also prime.
Mathematics Subject Classification ID: 06F35
zbMATH DE Number: 1563553
zbMATH Keywords: BCK-algebra
zbMATH Keywords: fuzzy ideal
reviewed by: Wiesław A. Dudek
MaRDI profile type: Publication
cites work: Q3988755
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cites work: Q4126337
cites work: Q4835100
cites work: Involutory and invertible fuzzy BCK-algebras
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full work available at URL: s0165-0114(98)00428-x
OpenAlex ID: W2058986219
description: scientific article; zbMATH DE number 1563553