Kernels of Residuated Maps as Complete Congruences in Lattices

Authors

Branimir Šešelja¹, Andreja Tepavčević^{1, 2, *,}

¹Department of Mathematics and Informatics, Faculty of Sciences, University of Novi Sad, Trg Dositeja Obradovića 4, Novi Sad, 21000, Serbia

²Mathematical Institute SASA Kneza Mihaila 35, Belgrade, 11000, Serbia

^*Corresponding author. Email: andreja@dmi.uns.ac.rs

DOI

10.2991/ijcis.d.200714.001How to use a DOI?

Keywords

Complete lattice; Lattice-valued fuzzy set; Congruence; Residuated map

Abstract

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.

Copyright

© 2020 The Authors. Published by Atlantis Press B.V.

Open Access

This is an open access article distributed under the CC BY-NC 4.0 license (http://creativecommons.org/licenses/by-nc/4.0/).

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TY  - JOUR
AU  - Branimir Šešelja
AU  - Andreja Tepavčević
PY  - 2020
DA  - 2020/07/20
TI  - Kernels of Residuated Maps as Complete Congruences in Lattices
JO  - International Journal of Computational Intelligence Systems
SP  - 966
EP  - 973
VL  - 13
IS  - 1
SN  - 1875-6883
UR  - https://doi.org/10.2991/ijcis.d.200714.001
DO  - 10.2991/ijcis.d.200714.001
ID  - Šešelja2020
ER  -