New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators

Tao Wu

Kybernetika (2024)

  • Volume: 60, Issue: 5, page 624-651
  • ISSN: 0023-5954

Abstract

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The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm T and a t-conorm S by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on L , we obtain new classes of uni-nullnorms on L via closure (interior) operators. The constructions of uni-nullnorms on some certain classes of bounded lattices can provide another different perspective of t-norms and the dual of t-norms, uninorms and some other associative aggregation operations on bounded lattices. That is, the constructions seem to be the ordinal like sum constructions, but not limited to the ordinal like sum constructions.

How to cite

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Wu, Tao. "New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators." Kybernetika 60.5 (2024): 624-651. <http://eudml.org/doc/299718>.

@article{Wu2024,
abstract = {The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm $T$ and a t-conorm $S$ by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on $L$, we obtain new classes of uni-nullnorms on $L$ via closure (interior) operators. The constructions of uni-nullnorms on some certain classes of bounded lattices can provide another different perspective of t-norms and the dual of t-norms, uninorms and some other associative aggregation operations on bounded lattices. That is, the constructions seem to be the ordinal like sum constructions, but not limited to the ordinal like sum constructions.},
author = {Wu, Tao},
journal = {Kybernetika},
keywords = {uni-nullnorm; nullnorm; closure operator; construction; bounded lattice; ordinal like sum construction},
language = {eng},
number = {5},
pages = {624-651},
publisher = {Institute of Information Theory and Automation AS CR},
title = {New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators},
url = {http://eudml.org/doc/299718},
volume = {60},
year = {2024},
}

TY - JOUR
AU - Wu, Tao
TI - New constructions of uni-nullnorms on certain classes of bounded lattices by closure (interior) operators
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
VL - 60
IS - 5
SP - 624
EP - 651
AB - The primary aim of this article is to put forward new classes of uni-nullnorms on certain classes of bounded lattices via closure (interior) operators. Due to the new classes of uninorms combining both a t-norm $T$ and a t-conorm $S$ by various kinds of closure operators or interior operators, the relationships and properties among the same class of uninorms on $L$, we obtain new classes of uni-nullnorms on $L$ via closure (interior) operators. The constructions of uni-nullnorms on some certain classes of bounded lattices can provide another different perspective of t-norms and the dual of t-norms, uninorms and some other associative aggregation operations on bounded lattices. That is, the constructions seem to be the ordinal like sum constructions, but not limited to the ordinal like sum constructions.
LA - eng
KW - uni-nullnorm; nullnorm; closure operator; construction; bounded lattice; ordinal like sum construction
UR - http://eudml.org/doc/299718
ER -

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