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

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