A T-partial order obtained from T-norms

Funda Karaçal; M. Nesibe Kesicioğlu

Kybernetika (2011)

  • Volume: 47, Issue: 2, page 300-314
  • ISSN: 0023-5954

Abstract

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A partial order on a bounded lattice L is called t-order if it is defined by means of the t-norm on L . It is obtained that for a t-norm on a bounded lattice L the relation a ⪯ T b iff a = T ( x , b ) for some x ∈ L is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of L and a complete lattice on the subset A of all elements of L which are the supremum of a subset of atoms.

How to cite

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Karaçal, Funda, and Kesicioğlu, M. Nesibe. "A T-partial order obtained from T-norms." Kybernetika 47.2 (2011): 300-314. <http://eudml.org/doc/196741>.

@article{Karaçal2011,
abstract = {A partial order on a bounded lattice $L$ is called t-order if it is defined by means of the t-norm on $L$. It is obtained that for a t-norm on a bounded lattice $L$ the relation $a\preceq _\{T\}b$ iff $a=T(x,b)$ for some $x\in L$ is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of $L$ and a complete lattice on the subset $A$ of all elements of $L$ which are the supremum of a subset of atoms.},
author = {Karaçal, Funda, Kesicioğlu, M. Nesibe},
journal = {Kybernetika},
keywords = {triangular norm; bounded lattice; triangular action; $\bigvee $-distributive; idempotent element; triangular norm; bounded lattice; triangular action; -distributive; idempotent element},
language = {eng},
number = {2},
pages = {300-314},
publisher = {Institute of Information Theory and Automation AS CR},
title = {A T-partial order obtained from T-norms},
url = {http://eudml.org/doc/196741},
volume = {47},
year = {2011},
}

TY - JOUR
AU - Karaçal, Funda
AU - Kesicioğlu, M. Nesibe
TI - A T-partial order obtained from T-norms
JO - Kybernetika
PY - 2011
PB - Institute of Information Theory and Automation AS CR
VL - 47
IS - 2
SP - 300
EP - 314
AB - A partial order on a bounded lattice $L$ is called t-order if it is defined by means of the t-norm on $L$. It is obtained that for a t-norm on a bounded lattice $L$ the relation $a\preceq _{T}b$ iff $a=T(x,b)$ for some $x\in L$ is a partial order. The goal of the paper is to determine some conditions such that the new partial order induces a bounded lattice on the subset of all idempotent elements of $L$ and a complete lattice on the subset $A$ of all elements of $L$ which are the supremum of a subset of atoms.
LA - eng
KW - triangular norm; bounded lattice; triangular action; $\bigvee $-distributive; idempotent element; triangular norm; bounded lattice; triangular action; -distributive; idempotent element
UR - http://eudml.org/doc/196741
ER -

References

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Citations in EuDML Documents

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  1. Emel Aşıcı, Funda Karaçal, Incomparability with respect to the triangular order
  2. M. Nesibe Kesicioğlu, About the equivalence of nullnorms on bounded lattice
  3. Lifeng Li, Jianke Zhang, Chang Zhou, Sufficient conditions for a T-partial order obtained from triangular norms to be a lattice
  4. M. Nesibe Kesicioğlu, Ü. Ertuğrul, F. Karaçal, Some notes on U-partial order
  5. Emel Aşıcı, Radko Mesiar, On the direct product of uninorms on bounded lattices
  6. Funda Karaçal, Ümit Ertuğrul, M. Nesibe Kesicioğlu, An extension method for t-norms on subintervals to t-norms on bounded lattices
  7. Mourad Yettou, Abdelaziz Amroune, Lemnaouar Zedam, A binary operation-based representation of a lattice
  8. Emel Aşıcı, An extension of the ordering based on nullnorms

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