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https://open.uns.ac.rs/handle/123456789/20603
Title: | Kernels of residuated maps as complete congruences in lattices | Authors: | Šešelja Branimir Tepavčević Andreja |
Issue Date: | 2020 | Journal: | International Journal of Computational Intelligence Systems | Abstract: | © 2020 The Authors. Published by Atlantis Press B.V. 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. | URI: | https://open.uns.ac.rs/handle/123456789/20603 | ISSN: | 1875-6883 | DOI: | 10.2991/ijcis.d.200714.001 |
Appears in Collections: | PMF Publikacije/Publications |
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