Authors: Šešelja, Branimir
Tepavčević, Andreja 
Affiliations: Mathematical Institute of the Serbian Academy of Sciences and Arts 
Title: Kernels of residuated maps as complete congruences in lattices
Journal: International Journal of Computational Intelligence Systems
Volume: 13
Issue: 1
First page: 966
Last page: 973
Issue Date: 2020
Rank: M22
ISSN: 1875-6891
DOI: 10.2991/ijcis.d.200714.001
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.
Keywords: Complete lattice | Congruence | Lattice-valued fuzzy set | Residuated map
Publisher: Atlantis Press

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