On (\(\in,\in \vee q\))-fuzzy filters of BL-algebras
type: Item
instance of: scholarly article
title: On (\(\in,\in \vee q\))-fuzzy filters of BL-algebras
zbMATH Open document ID: 1184.03066
author: Xueling Ma
author: Jianming Zhan
published in: Journal of Systems Science and Complexity
publication date: 2009-10-23T00:00:00Z
review text: In this paper, the authors give the notions of \((\in ,\in \vee q)\)-fuzzy Boolean (implicative; positive implicative and fantastic) filters in BL-algebras and investigate some related properties. Some characterizations of these generalized fuzzy filters are derived. Finally, they discuss the relations among these generalized fuzzy filters and prove that an interval-valued \((\in ,\in \vee q)\)-fuzzy filter of a BL-algebra is Boolean (implicative) if and only if it is both positive implicative and fantastic.
reviewed by: Dana Piciu
Mathematics Subject Classification ID: 03G25
Mathematics Subject Classification ID: 06D35
zbMATH DE Number: 5620234
zbMATH Keywords: BL-algebra
zbMATH Keywords: fuzzy filter
zbMATH Keywords: implicative filter
zbMATH Keywords: fantastic filter
MaRDI profile type: Publication
full work available at URL: s11424-008-9073-2
OpenAlex ID: W2398883180
cites work: Metamathematics of fuzzy logic
cites work: Algebraic Analysis of Many Valued Logics
cites work: Q4693586
cites work: Q4275476
cites work: MV-algebras, BL-algebras, \(R_0\)-algebras, and multiple-valued logic.
cites work: On the logic foundation of fuzzy reasoning
cites work: Mathematics behind fuzzy logic
cites work: Q4506244
cites work: Q4542641
cites work: Boolean deductive systems of BL-algebras
cites work: Some types of filters in BL algebras
cites work: Fuzzy sets
cites work: Fuzzy filters of BL-algebras
cites work: A decision tree solution considering the decision maker's attitude
cites work: On fuzzy filters and fuzzy ideals of BL-algebras
cites work: \((\in,\in\vee\;q)\)-fuzzy subgroup
cites work: Fuzzy topology. I: Neighborhood structure of a fuzzy point and Moore-Smith convergence
cites work: \((\in,\in\!\vee q)\)-fuzzy subnear-rings and ideals.
cites work: Boolean products of BL-algebras
cites work: Compact representations of BL-algebras
cites work: Monoidal t-norm based logic: Towards a logic for left-continuous t-norms
cites work: \((\in,\in \vee q)\)-fuzzy normal, quasinormal and maximal subgroups
cites work: Generalized fuzzy groups and many-valued implications
DOI: 10.1007/S11424-008-9073-2
description: scientific article; zbMATH DE number 5620234