The MacNeille Completions for Residuated S-Posets

Result code in IS VaVaI
<a href="https://www.isvavai.cz/riv?ss=detail&h=RIV%2F00216224%3A14310%2F21%3A00119009" target="_blank" >RIV/00216224:14310/21:00119009 - isvavai.cz</a>
Result on the web
<a href="https://doi.org/10.1007/s10773-019-04046-2" target="_blank" >https://doi.org/10.1007/s10773-019-04046-2</a>
DOI - Digital Object Identifier
<a href="http://dx.doi.org/10.1007/s10773-019-04046-2" target="_blank" >10.1007/s10773-019-04046-2</a>

Result language
angličtina
Original language name
The MacNeille Completions for Residuated S-Posets
Original language description
In this paper, we continue the study of injectivity for fuzzy-like structures. We extend the results of Zhang and Paseka for S-semigroups to the setting of residuated S-posets. It turns out that every residuated S-poset over a quantale S embeds into its MacNeille completion as its E⩽-injective hull. In particular, if S is a commutative quantale, then the injectives in the category of residuated S-posets with subhomomorphisms are precisely the quantale algebras introduced by Solovyov. Quantale algebras provide a convenient universally algebraic framework for developing lattice-valued analogues of fuzzification.
Czech name
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Czech description
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Type
J<sub>imp</sub> - Article in a specialist periodical, which is included in the Web of Science database
CEP classification
—
OECD FORD branch
10101 - Pure mathematics

Project
<a href="/en/project/GA18-06915S" target="_blank" >GA18-06915S: New approaches to aggregation operators in analysis and processing of data</a><br>
Continuities
P - Projekt vyzkumu a vyvoje financovany z verejnych zdroju (s odkazem do CEP)

Publication year
2021
Confidentiality
S - Úplné a pravdivé údaje o projektu nepodléhají ochraně podle zvláštních právních předpisů

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