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dc.contributor.authorRay, Suryansu
dc.date.accessioned2007-09-14T09:22:32Z
dc.date.available2007-09-14T09:22:32Z
dc.date.issued1997
dc.identifier.issn1134-5632
dc.identifier.urihttp://hdl.handle.net/2099/3482
dc.description.abstractGiven a complete and atomic Boolean algebra $B$, there exists a family $\tau_{\gamma}$ of triangular norms on $B$ such that, under the partial ordering of triangular norms, $\tau_{\gamma}$ is a Boolean algebra isomorphic to $B$, where $\gamma$ is the set of all atoms in $B$. In other words, as we have shown in this note, every complete and atomic Boolean algebra can be represented by its own triangular norms. What we have not shown in this paper is our belief that $\tau_{\gamma}$ is not unique for $B$ and that, for such a representation, $B$ needs neither to be complete, nor to be atomic.
dc.format.extent63-68
dc.language.isoeng
dc.publisherUniversitat Politècnica de Catalunya. Secció de Matemàtiques i Informàtica
dc.relation.ispartofMathware & soft computing . 1997 Vol. 4 Núm. 1
dc.rightsReconeixement-NoComercial-CompartirIgual 3.0 Espanya
dc.rights.urihttp://creativecommons.org/licenses/by-nc-nd/3.0/es/
dc.subject.otherTriangular norms
dc.subject.otherComplete and atomic Boolean algebra
dc.subject.otherFuzzy groups
dc.titleRepresentation of a Boolean algebra by its triangular norms
dc.typeArticle
dc.subject.lemacAnells booleans
dc.subject.amsClassificació AMS::06 Order, lattices, ordered algebraic structures::06E Boolean algebras (Boolean rings)
dc.subject.amsClassificació AMS::46 Associative rings and algebras::46H Topological algebras, normed rings and algebras, Banach algebras
dc.rights.accessOpen Access


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