On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices

Emel Aşıcı

Kybernetika (2022)

  • Volume: 58, Issue: 3, page 456-478
  • ISSN: 0023-5954

Abstract

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Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices.

How to cite

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Aşıcı, Emel. "On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices." Kybernetika 58.3 (2022): 456-478. <http://eudml.org/doc/298905>.

@article{Aşıcı2022,
abstract = {Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices.},
author = {Aşıcı, Emel},
journal = {Kybernetika},
keywords = {t-norm; t-conorm; ordinal sum; bounded lattice},
language = {eng},
number = {3},
pages = {456-478},
publisher = {Institute of Information Theory and Automation AS CR},
title = {On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices},
url = {http://eudml.org/doc/298905},
volume = {58},
year = {2022},
}

TY - JOUR
AU - Aşıcı, Emel
TI - On the construction of t-norms (t-conorms) by using interior (closure) operator on bounded lattices
JO - Kybernetika
PY - 2022
PB - Institute of Information Theory and Automation AS CR
VL - 58
IS - 3
SP - 456
EP - 478
AB - Recently, the topic of construction methods for triangular norms (triangular conorms), uninorms, nullnorms, etc. has been studied widely. In this paper, we propose construction methods for triangular norms (t-norms) and triangular conorms (t-conorms) on bounded lattices by using interior and closure operators, respectively. Thus, we obtain some proposed methods given by Ertuğrul, Karaçal, Mesiar [15] and Çaylı [8] as results. Also, we give some illustrative examples. Finally, we conclude that the introduced construction methods can not be generalized by induction to a modified ordinal sum for t-norms and t-conorms on bounded lattices.
LA - eng
KW - t-norm; t-conorm; ordinal sum; bounded lattice
UR - http://eudml.org/doc/298905
ER -

References

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