Nuclei and conuclei on Girard posets

D 2019

Nuclei and conuclei on Girard posets

PASEKA, Jan and David KRUML

Basic information

Original name

Nuclei and conuclei on Girard posets

Authors

PASEKA, Jan (203 Czech Republic, guarantor, belonging to the institution) and David KRUML (203 Czech Republic, belonging to the institution)

Edition

Neuveden, Atlantis Studies in Uncertainty Modelling, volume 1, p. 289-296, 8 pp. 2019

Publisher

Atlantis Press

Other information

Language

English

Type of outcome

Stať ve sborníku

Field of Study

10101 Pure mathematics

Country of publisher

France

Confidentiality degree

není předmětem státního či obchodního tajemství

Publication form

electronic version available online

References:

URL

RIV identification code

RIV/00216224:14310/19:00108213

Organization unit

Faculty of Science

ISBN

978-94-6252-770-6

ISSN

DOI

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

UT WoS

000558710000042

Keywords in English

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

Abstract

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.

Links

GA18-06915S, research and development project

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

Investor: Czech Science Foundation

MUNI/G/1211/2017, interní kód MU

Name: Grupové techniky a kvantová informace (Acronym: GRUPIK)

Investor: Masaryk University, INTERDISCIPLINARY - Interdisciplinary research projects

Citovat

PASEKA, Jan and 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, p. 289-296. ISBN 978-94-6252-770-6. Available from: 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 and 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, p.~289-296. ISBN~978-94-6252-770-6. Available from: https://dx.doi.org/10.2991/eusflat-19.2019.42.

Detailed Information on Publication Record