Fuzzy multiply positive implicative hyper BCK-ideals of hyper BCK-algebras
type: Item
instance of: scholarly article
title: Fuzzy multiply positive implicative hyper BCK-ideals of hyper BCK-algebras
zbMATH Open document ID: 1067.06018
DOI: 10.1155/S0161171204306186
author: Jianming Zhan
author: Dajing Xiang
author: Zhisong Tan
published in: International Journal of Mathematics and Mathematical Sciences
publication date: 2005-05-18T00:00:00Z
full work available at URL: https://eudml.org/doc/51457
review text: In a hyper BCK-algebra \((H,\circ,0)\) the symbol \(x\circ y^n\) denotes \((\dots((x\circ y)\circ y)\circ\ldots)\circ y\), where \(y\) is used \(n\) times. A nonempty subset \(I\) of \(H\) is a multiply positive implicative hyper BCK-ideal if \(0\in I\) and for any \(x,y,z\in H\) such that \((x\circ y)\circ z^n\ll I\) and \(y\circ z^m\ll I\) there exists a natural number \(k=k(x,y,z)\) for which \(x\circ z^k\ll I\). Fuzzification of ideals defined in this way is presented. A part of the results are an extension of results obtained by \textit{W. A. Dudek, Y. B. Jun}, and \textit{Z. Stojaković} [Fuzzy Sets Syst. 123, 251--258 (2001; Zbl 1018.06016)] to the case of hyper BCK-algebras.
reviewed by: Wiesław A. Dudek
Mathematics Subject Classification ID: 06F35
Mathematics Subject Classification ID: 03G25
zbMATH DE Number: 2168677
zbMATH Keywords: hyper BCK-algebra
zbMATH Keywords: hyper ideal
zbMATH Keywords: fuzzy set
MaRDI profile type: Publication
description: scientific article; zbMATH DE number 2168677