Characterization of the order induced by uninorm with the underlying drastic product or drastic sum

Zhi-qiang Liu

Kybernetika (2024)

  • Volume: 60, Issue: 6, page 723-739
  • ISSN: 0023-5954

Abstract

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In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained.

How to cite

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Liu, Zhi-qiang. "Characterization of the order induced by uninorm with the underlying drastic product or drastic sum." Kybernetika 60.6 (2024): 723-739. <http://eudml.org/doc/299885>.

@article{Liu2024,
abstract = {In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained.},
author = {Liu, Zhi-qiang},
journal = {Kybernetika},
keywords = {uninorm; triangular norm; divisibility; partial order; distributive lattice},
language = {eng},
number = {6},
pages = {723-739},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Characterization of the order induced by uninorm with the underlying drastic product or drastic sum},
url = {http://eudml.org/doc/299885},
volume = {60},
year = {2024},
}

TY - JOUR
AU - Liu, Zhi-qiang
TI - Characterization of the order induced by uninorm with the underlying drastic product or drastic sum
JO - Kybernetika
PY - 2024
PB - Institute of Information Theory and Automation AS CR
VL - 60
IS - 6
SP - 723
EP - 739
AB - In this article, we investigate the algebraic structures of the partial orders induced by uninorms on a bounded lattice. For a class of uninorms with the underlying drastic product or drastic sum, we first present some conditions making a bounded lattice also a lattice with respect to the order induced by such uninorms. And then we completely characterize the distributivity of the lattices obtained.
LA - eng
KW - uninorm; triangular norm; divisibility; partial order; distributive lattice
UR - http://eudml.org/doc/299885
ER -

References

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