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Soft Computing
Published in: Soft Computing 3/2013

01-03-2013 | Original Paper

On the algebraic structure of binary lattice-valued fuzzy relations

Authors: Xiaodong Pan, Yang Xu

Published in: Soft Computing | Issue 3/2013

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Abstract

From a general algebraic point of view, this paper aims at providing an algebraic analysis for binary lattice-valued relations based on lattice implication algebras—a kind of lattice-valued propositional logical algebra. By abstracting away from the concrete lattice-valued relations and the operations on them, such as composition and converse, the notion of lattice-valued relation algebra is introduced, LRA for short. The reduct of an LRA is a lattice implication algebra. Such an algebra generalizes Boolean relation algebras by general distributive lattices and can provide a fundamental algebraic theory for establishing lattice-valued first-order logic. Some important results are generalized from the classical case. The notion of cylindric filter is introduced and the generated cylindric filters are characterized.
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Metadata
Title
On the algebraic structure of binary lattice-valued fuzzy relations
Authors
Xiaodong Pan
Yang Xu
Publication date
01-03-2013
Publisher
Springer-Verlag
Published in
Soft Computing / Issue 3/2013
Print ISSN: 1432-7643
Electronic ISSN: 1433-7479
DOI
https://doi.org/10.1007/s00500-012-0916-3

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