An extension method for t-norms on subintervals to t-norms on bounded lattices

Funda Karaçal; Ümit Ertuğrul; M. Nesibe Kesicioğlu

Kybernetika (2019)

  • Volume: 55, Issue: 6, page 976-993
  • ISSN: 0023-5954

Abstract

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In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on from the t-norm on a subinterval of need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.

How to cite

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Karaçal, Funda, Ertuğrul, Ümit, and Kesicioğlu, M. Nesibe. "An extension method for t-norms on subintervals to t-norms on bounded lattices." Kybernetika 55.6 (2019): 976-993. <http://eudml.org/doc/297135>.

@article{Karaçal2019,
abstract = {In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.},
author = {Karaçal, Funda, Ertuğrul, Ümit, Kesicioğlu, M. Nesibe},
journal = {Kybernetika},
keywords = {T-norm; bounded lattice; construction method; subinterval},
language = {eng},
number = {6},
pages = {976-993},
publisher = {Institute of Information Theory and Automation AS CR},
title = {An extension method for t-norms on subintervals to t-norms on bounded lattices},
url = {http://eudml.org/doc/297135},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Karaçal, Funda
AU - Ertuğrul, Ümit
AU - Kesicioğlu, M. Nesibe
TI - An extension method for t-norms on subintervals to t-norms on bounded lattices
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 6
SP - 976
EP - 993
AB - In this paper, a construction method on a bounded lattice obtained from a given t-norm on a subinterval of the bounded lattice is presented. The supremum distributivity of the constructed t-norm by the mentioned method is investigated under some special conditions. It is shown by an example that the extended t-norm on $L$ from the t-norm on a subinterval of $L$ need not be a supremum-distributive t-norm. Moreover, some relationships between the mentioned construction method and the other construction methods in the literature are presented.
LA - eng
KW - T-norm; bounded lattice; construction method; subinterval
UR - http://eudml.org/doc/297135
ER -

References

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