\(TL\)-filters of integral residuated \(l\)-monoids
type: Item
instance of: scholarly article
title: \(TL\)-filters of integral residuated \(l\)-monoids
zbMATH Open document ID: 1119.06010
author: Zhudeng Wang
published in: Information Sciences
publication date: 2007-02-16T00:00:00Z
review text: The paper deals with a fuzzification of filters on integral residuated lattice-ordered monoids. Analogously to the crisp case, a description of the fuzzy filter generated by a fuzzy subset is given. Then the relation between fuzzy filters and homomorphisms in the underlying variety is discussed. In particular, an image of a fuzzy filter under a homomorphism is a fuzzy filter. The same is true also for preimages of fuzzy filters. Finally, it is shown that there is a correspondence between the set of fuzzy filters and the set of \(T\)-congruences. More precisely, it is proved that each fuzzy filter induces a \(T\)-congruence and vice versa.
Mathematics Subject Classification ID: 06F05
Mathematics Subject Classification ID: 08A72
zbMATH DE Number: 5127727
zbMATH Keywords: fuzzy filter
zbMATH Keywords: integral residuated \(l\)-monoid
zbMATH Keywords: \(T\)-congruence
reviewed by: Rostislav Horčík
MaRDI profile type: Publication
full work available at URL: j.ins.2006.03.019
OpenAlex ID: W2007772986
cites work: Q5331549
cites work: Foundations of fuzzy functions and vague algebra based on many-valued equivalence relations, part I: fuzzy functions and their applications
cites work: Monoidal t-norm based logic: Towards a logic for left-continuous t-norms
cites work: Metamathematics of fuzzy logic
cites work: Q4836218
cites work: Fuzzy filters of MTL-algebras
cites work: Fuzzy bi-ideals in ordered semigroups
cites work: Fuzzy implicative and Boolean filters of \(R_{0}\) algebras
cites work: Fuzzy filters of BL-algebras
cites work: Fuzzy Boolean and positive implicative filters of BL-algebras
cites work: Boolean deductive systems of BL-algebras
cites work: On \(L\)-subsets and \(TL\)-subalgebras
cites work: On \(T\)-congruence \(L\)-relations on groups and rings
cites work: \(TL\)-subrings and \(TL\)-ideals. I: Basic concepts
cites work: Similarity relations and fuzzy orderings
DOI: 10.1016/J.INS.2006.03.019
description: scientific article; zbMATH DE number 5127727