ZL-Completions for ZL-Semigroups
In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where L is a complete residuated lattice. For this asymmetric mathematica...
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ftmdpi:oai:mdpi.com:/2073-8994/14/3/578/ 2023-08-20T04:06:09+02:00 ZL-Completions for ZL-Semigroups Shuhua Su Qingguo Li Qi Li 2022-03-15 application/pdf https://doi.org/10.3390/sym14030578 EN eng Multidisciplinary Digital Publishing Institute Mathematics and Symmetry/Asymmetry https://dx.doi.org/10.3390/sym14030578 https://creativecommons.org/licenses/by/4.0/ Symmetry; Volume 14; Issue 3; Pages: 578 fuzzy subset selection fuzzy order symmetry and asymmetry Z L -semigroup Z L -continuous mapping Z L -completion complete residuated lattice Text 2022 ftmdpi https://doi.org/10.3390/sym14030578 2023-08-01T04:27:47Z In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where L is a complete residuated lattice. For this asymmetric mathematical structure, we define a ZL-completion of it to be a complete residuated L-ordered semigroup together with a join-dense L-ordered semigroup embedding satisfying the universal property. We prove that: (1) For every compositive ZL, the category CSL of complete residuated L-ordered semigroups is a reflective subcategory of the category SZL of ZL-semigroups; (2) for an arbitrary ZL, there is an adjunction between SZL and the category SZL→E of weakly ZL-continuous L-ordered semigroup embeddings of ZL-semigroups. By appropriate specialization of ZL, the results can be applied to the DML-completion, certain completions associated with fuzzy subset systems, etc. Text DML MDPI Open Access Publishing Symmetry 14 3 578 |
institution |
Open Polar |
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MDPI Open Access Publishing |
op_collection_id |
ftmdpi |
language |
English |
topic |
fuzzy subset selection fuzzy order symmetry and asymmetry Z L -semigroup Z L -continuous mapping Z L -completion complete residuated lattice |
spellingShingle |
fuzzy subset selection fuzzy order symmetry and asymmetry Z L -semigroup Z L -continuous mapping Z L -completion complete residuated lattice Shuhua Su Qingguo Li Qi Li ZL-Completions for ZL-Semigroups |
topic_facet |
fuzzy subset selection fuzzy order symmetry and asymmetry Z L -semigroup Z L -continuous mapping Z L -completion complete residuated lattice |
description |
In this paper, we generalize a common completion pattern of ordered semigroups to the fuzzy setting. Based on a standard L-completion ZL, we introduce the notion of a ZL-semigroup as a generalization of an L-ordered semigroup, where L is a complete residuated lattice. For this asymmetric mathematical structure, we define a ZL-completion of it to be a complete residuated L-ordered semigroup together with a join-dense L-ordered semigroup embedding satisfying the universal property. We prove that: (1) For every compositive ZL, the category CSL of complete residuated L-ordered semigroups is a reflective subcategory of the category SZL of ZL-semigroups; (2) for an arbitrary ZL, there is an adjunction between SZL and the category SZL→E of weakly ZL-continuous L-ordered semigroup embeddings of ZL-semigroups. By appropriate specialization of ZL, the results can be applied to the DML-completion, certain completions associated with fuzzy subset systems, etc. |
format |
Text |
author |
Shuhua Su Qingguo Li Qi Li |
author_facet |
Shuhua Su Qingguo Li Qi Li |
author_sort |
Shuhua Su |
title |
ZL-Completions for ZL-Semigroups |
title_short |
ZL-Completions for ZL-Semigroups |
title_full |
ZL-Completions for ZL-Semigroups |
title_fullStr |
ZL-Completions for ZL-Semigroups |
title_full_unstemmed |
ZL-Completions for ZL-Semigroups |
title_sort |
zl-completions for zl-semigroups |
publisher |
Multidisciplinary Digital Publishing Institute |
publishDate |
2022 |
url |
https://doi.org/10.3390/sym14030578 |
genre |
DML |
genre_facet |
DML |
op_source |
Symmetry; Volume 14; Issue 3; Pages: 578 |
op_relation |
Mathematics and Symmetry/Asymmetry https://dx.doi.org/10.3390/sym14030578 |
op_rights |
https://creativecommons.org/licenses/by/4.0/ |
op_doi |
https://doi.org/10.3390/sym14030578 |
container_title |
Symmetry |
container_volume |
14 |
container_issue |
3 |
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578 |
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1774717095157694464 |