The MacNeille Completions for Residuated S-Posets

J 2021

The MacNeille Completions for Residuated S-Posets

ZHANG, Xia a Jan PASEKA

Základní údaje

Originální název

The MacNeille Completions for Residuated S-Posets

Autoři

ZHANG, Xia a Jan PASEKA

Vydání

International Journal of Theoretical Physics, New York, Springer, 2021, 0020-7748

Další údaje

Jazyk

angličtina

Typ výsledku

Článek v odborném periodiku

Obor

10101 Pure mathematics

Stát vydavatele

Spojené státy

Utajení

není předmětem státního či obchodního tajemství

Odkazy

URL

Impakt faktor

Impact factor: 1.308

Označené pro přenos do RIV

Ano

Kód RIV

RIV/00216224:14310/21:00119009

Organizační jednotka

Přírodovědecká fakulta

Klíčová slova anglicky

Residuated poset; S-semigroup; Residuated S-poset; Order-embedding; Subhomomorphism; Lattice-valued sup-lattice; Sup-algebra; Quantale; Q-module; Q-algebra; S-semigroup quantale; Injective object; Injective hull

Štítky

14311010, rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 10. 6. 2021 09:34, Mgr. Marie Novosadová Šípková, DiS.

Anotace

V originále

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.

Návaznosti

GA18-06915S, projekt VaV

Název: Nové přístupy k agregačním operátorům v analýze a zpracování dat

Investor: Grantová agentura ČR, Nové přístupy k agregačním operátorům v analýze a zpracování dat

Citovat

ZHANG, Xia a Jan PASEKA. The MacNeille Completions for Residuated S-Posets. International Journal of Theoretical Physics. New York: Springer, 2021, roč. 60, č. 2, s. 667-676. ISSN 0020-7748. Dostupné z: https://doi.org/10.1007/s10773-019-04046-2.

@article{1775038,
   author = {Zhang, Xia and Paseka, Jan},
   article_location = {New York},
   article_number = {2},
   doi = {https://doi.org/10.1007/s10773-019-04046-2},
   keywords = {Residuated poset; S-semigroup; Residuated S-poset; Order-embedding; Subhomomorphism; Lattice-valued sup-lattice; Sup-algebra; Quantale; Q-module; Q-algebra; S-semigroup quantale; Injective object; Injective hull},
   language = {eng},
   issn = {0020-7748},
   journal = {International Journal of Theoretical Physics},
   title = {The MacNeille Completions for Residuated S-Posets},
   url = {https://doi.org/10.1007/s10773-019-04046-2},
   volume = {60},
   year = {2021}
}

TY  - JOUR
ID  - 1775038
AU  - Zhang, Xia - Paseka, Jan
PY  - 2021
TI  - The MacNeille Completions for Residuated S-Posets
JF  - International Journal of Theoretical Physics
VL  - 60
IS  - 2
SP  - 667-676
EP  - 667-676
PB  - Springer
SN  - 00207748
KW  - Residuated poset
KW  - S-semigroup
KW  - Residuated S-poset
KW  - Order-embedding
KW  - Subhomomorphism
KW  - Lattice-valued sup-lattice
KW  - Sup-algebra
KW  - Quantale
KW  - Q-module
KW  - Q-algebra
KW  - S-semigroup quantale
KW  - Injective object
KW  - Injective hull
UR  - https://doi.org/10.1007/s10773-019-04046-2
N2  - 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.
ER  -

ZHANG, Xia a Jan PASEKA. The MacNeille Completions for Residuated S-Posets. \textit{International Journal of Theoretical Physics}. New York: Springer, 2021, roč.~60, č.~2, s.~667-676. ISSN~0020-7748. Dostupné z: https://doi.org/10.1007/s10773-019-04046-2.

Přehled o publikaci