Nuclei and conuclei on Girard posets

D 2019

Nuclei and conuclei on Girard posets

PASEKA, Jan a David KRUML

Základní údaje

Originální název

Nuclei and conuclei on Girard posets

Autoři

PASEKA, Jan (203 Česká republika, garant, domácí) a David KRUML (203 Česká republika, domácí)

Vydání

Neuveden, Atlantis Studies in Uncertainty Modelling, volume 1, od s. 289-296, 8 s. 2019

Nakladatel

Atlantis Press

Další údaje

Jazyk

angličtina

Typ výsledku

Stať ve sborníku

Obor

10101 Pure mathematics

Stát vydavatele

Francie

Utajení

není předmětem státního či obchodního tajemství

Forma vydání

elektronická verze "online"

Odkazy

URL

Kód RIV

RIV/00216224:14310/19:00108213

Organizační jednotka

Přírodovědecká fakulta

ISBN

978-94-6252-770-6

ISSN

DOI

http://dx.doi.org/10.2991/eusflat-19.2019.42

UT WoS

000558710000042

Klíčová slova anglicky

Residuated poset; Frobenius poset; Girard poset; Girard quantale; quantic nucleus; quantic conucleus; ideal conucleus

Štítky

rivok

Příznaky

Mezinárodní význam, Recenzováno

Změněno: 20. 1. 2021 11:05, Mgr. Marie Šípková, DiS.

Anotace

V originále

It is well-known that the semantics of a given fuzzy logic can be formally axiomatized by means of a residuated poset. Based on a notion of dualizing (cyclic) element we introduce the notion of a Frobenius (Girard) poset. With this paper we hope to contribute to the theory of Frobenius posets and Girard posets. By means of a dualizing element we establish a one-to-one correspondence between a Frobenius poset and its opposite which is again a Frobenius poset. We also investigate some properties of nuclei and conuclei on Girard posets. Finally, we discuss the relation between quantic nuclei and ideal conuclei on a Girard poset and its opposite. We show that they are in one-to-one correspondence.

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

MUNI/G/1211/2017, interní kód MU

Název: Grupové techniky a kvantová informace (Akronym: GRUPIK)

Investor: Masarykova univerzita, Grupové techniky a kvantová informace, INTERDISCIPLINARY - Mezioborové výzkumné projekty

Citovat

PASEKA, Jan a David KRUML. Nuclei and conuclei on Girard posets. Online. In Vilém Novák, Vladimír Mařík, Martin Štěpnička, Mirko Navara, Petr Hurtík,. Atlantis Studies in Uncertainty Modelling, volume 1. Neuveden: Atlantis Press, 2019, s. 289-296. ISBN 978-94-6252-770-6. Dostupné z: https://dx.doi.org/10.2991/eusflat-19.2019.42.

@inproceedings{1640578,
   author = {Paseka, Jan and Kruml, David},
   address = {Neuveden},
   booktitle = {Atlantis Studies in Uncertainty Modelling, volume 1},
   doi = {http://dx.doi.org/10.2991/eusflat-19.2019.42},
   editor = {Vilém Novák, Vladimír Mařík, Martin Štěpnička, Mirko Navara, Petr Hurtík,},
   keywords = {Residuated poset; Frobenius poset; Girard poset; Girard quantale; quantic nucleus; quantic conucleus; ideal conucleus},
   howpublished = {elektronická verze "online"},
   language = {eng},
   location = {Neuveden},
   isbn = {978-94-6252-770-6},
   pages = {289-296},
   publisher = {Atlantis Press},
   title = {Nuclei and conuclei on Girard posets},
   url = {https://download.atlantis-press.com/article/125914812.pdf},
   year = {2019}
}

TY  - JOUR
ID  - 1640578
AU  - Paseka, Jan - Kruml, David
PY  - 2019
TI  - Nuclei and conuclei on Girard posets
PB  - Atlantis Press
CY  - Neuveden
SN  - 9789462527706
KW  - Residuated poset
KW  - Frobenius poset
KW  - Girard poset
KW  - Girard quantale
KW  - quantic nucleus
KW  - quantic conucleus
KW  - ideal conucleus
UR  - https://download.atlantis-press.com/article/125914812.pdf
L2  - https://download.atlantis-press.com/article/125914812.pdf
N2  - It is well-known that the semantics of a given fuzzy logic can be formally axiomatized by means of a residuated poset. Based on a notion of dualizing (cyclic) element we introduce the notion of a Frobenius (Girard) poset. With this paper we hope to contribute to the theory of Frobenius posets and Girard posets. By means of a dualizing element we establish a one-to-one correspondence between a Frobenius poset and its opposite which is again a Frobenius poset. We also investigate some properties of nuclei and conuclei on Girard posets. Finally, we discuss the relation between quantic nuclei and ideal conuclei on a Girard poset and its opposite. We show that they are in one-to-one correspondence.
ER  -

PASEKA, Jan a David KRUML. Nuclei and conuclei on Girard posets. Online. In Vilém Novák, Vladimír Mařík, Martin Štěpnička, Mirko Navara, Petr Hurtík,. \textit{Atlantis Studies in Uncertainty Modelling, volume 1}. Neuveden: Atlantis Press, 2019, s.~289-296. ISBN~978-94-6252-770-6. Dostupné z: https://dx.doi.org/10.2991/eusflat-19.2019.42.

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