| 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. |
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@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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