Kernels of Residuated Maps as Complete Congruences in Lattices

In a context of lattice-valued functions (also called lattice-valued fuzzy sets), where the codomain is a complete lattice L, an equivalence relation defined on L by the equality of related cuts is investigated. It is known that this relation is a complete congruence on the join-semilattice reduct o...

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Main Authors:	Branimir Šešelja, Andreja Tepavčević
Format:	Article
Language:	English
Published:	Atlantis Press 2020-07-01
Series:	International Journal of Computational Intelligence Systems
Subjects:	Complete lattice Lattice-valued fuzzy set Congruence Residuated map
Online Access:	https://www.atlantis-press.com/article/125941886/view

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spelling	doaj-8e676c480c9f46859b527ee8555088e22020-11-25T03:37:11ZengAtlantis PressInternational Journal of Computational Intelligence Systems 1875-68832020-07-0113110.2991/ijcis.d.200714.001Kernels of Residuated Maps as Complete Congruences in LatticesBranimir ŠešeljaAndreja TepavčevićIn a context of lattice-valued functions (also called lattice-valued fuzzy sets), where the codomain is a complete lattice L, an equivalence relation defined on L by the equality of related cuts is investigated. It is known that this relation is a complete congruence on the join-semilattice reduct of L. In terms of residuated maps, necessary and sufficient conditions under which this equivalence is a complete congruence on L are given. In the same framework of residuated maps, some known representation theorems for lattices and also for lattice-valued fuzzy sets are formulated in a new way. As a particular application of the obtained results, a representation theorem of finite lattices by meet-irreducible elements is given.https://www.atlantis-press.com/article/125941886/viewComplete latticeLattice-valued fuzzy setCongruenceResiduated map
collection	DOAJ
language	English
format	Article
sources	DOAJ
author	Branimir Šešelja Andreja Tepavčević
spellingShingle	Branimir Šešelja Andreja Tepavčević Kernels of Residuated Maps as Complete Congruences in Lattices International Journal of Computational Intelligence Systems Complete lattice Lattice-valued fuzzy set Congruence Residuated map
author_facet	Branimir Šešelja Andreja Tepavčević
author_sort	Branimir Šešelja
title	Kernels of Residuated Maps as Complete Congruences in Lattices
title_short	Kernels of Residuated Maps as Complete Congruences in Lattices
title_full	Kernels of Residuated Maps as Complete Congruences in Lattices
title_fullStr	Kernels of Residuated Maps as Complete Congruences in Lattices
title_full_unstemmed	Kernels of Residuated Maps as Complete Congruences in Lattices
title_sort	kernels of residuated maps as complete congruences in lattices
publisher	Atlantis Press
series	International Journal of Computational Intelligence Systems
issn	1875-6883
publishDate	2020-07-01
description	In a context of lattice-valued functions (also called lattice-valued fuzzy sets), where the codomain is a complete lattice L, an equivalence relation defined on L by the equality of related cuts is investigated. It is known that this relation is a complete congruence on the join-semilattice reduct of L. In terms of residuated maps, necessary and sufficient conditions under which this equivalence is a complete congruence on L are given. In the same framework of residuated maps, some known representation theorems for lattices and also for lattice-valued fuzzy sets are formulated in a new way. As a particular application of the obtained results, a representation theorem of finite lattices by meet-irreducible elements is given.
topic	Complete lattice Lattice-valued fuzzy set Congruence Residuated map
url	https://www.atlantis-press.com/article/125941886/view
work_keys_str_mv	AT branimirseselja kernelsofresiduatedmapsascompletecongruencesinlattices AT andrejatepavcevic kernelsofresiduatedmapsascompletecongruencesinlattices
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Kernels of Residuated Maps as Complete Congruences in Lattices

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