A principal topology obtained from uninorms

Funda Karaçal; Tuncay Köroğlu

Kybernetika (2022)

  • Volume: 58, Issue: 6, page 863-882
  • ISSN: 0023-5954

Abstract

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We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms.

How to cite

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Karaçal, Funda, and Köroğlu, Tuncay. "A principal topology obtained from uninorms." Kybernetika 58.6 (2022): 863-882. <http://eudml.org/doc/299400>.

@article{Karaçal2022,
abstract = {We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms.},
author = {Karaçal, Funda, Köroğlu, Tuncay},
journal = {Kybernetika},
keywords = {uninorm; closure operator; principal topology; bounded lattice},
language = {eng},
number = {6},
pages = {863-882},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A principal topology obtained from uninorms},
url = {http://eudml.org/doc/299400},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Karaçal, Funda
AU - Köroğlu, Tuncay
TI - A principal topology obtained from uninorms
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 6
SP - 863
EP - 882
AB - We obtain a principal topology and some related results. We also give some hints of possible applications. Some mathematical systems are both lattice and topological space. We show that a topology defined on the any bounded lattice is definable in terms of uninorms. Also, we see that these topologies satisfy the condition of the principal topology. These topologies can not be metrizable except for the discrete metric case. We show an equivalence relation on the class of uninorms on a bounded lattice based on equality of the topologies induced by uninorms.
LA - eng
KW - uninorm; closure operator; principal topology; bounded lattice
UR - http://eudml.org/doc/299400
ER -

References

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