Some methods to obtain t-norms and t-conorms on bounded lattices

Gül Deniz Çaylı

Kybernetika (2019)

  • Volume: 55, Issue: 2, page 273-294
  • ISSN: 0023-5954

Abstract

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In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice L based on a priori given t-norm acting on [ a , 1 ] and t-conorm acting on [ 0 , a ] for an arbitrary element a ∈ L ∖ { 0 , 1 } . We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.

How to cite

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Çaylı, Gül Deniz. "Some methods to obtain t-norms and t-conorms on bounded lattices." Kybernetika 55.2 (2019): 273-294. <http://eudml.org/doc/294262>.

@article{Çaylı2019,
abstract = {In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice $L$ based on a priori given t-norm acting on $ [a,1]$ and t-conorm acting on $[0,a]$ for an arbitrary element $a\in L\backslash \lbrace 0,1\rbrace $. We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.},
author = {Çaylı, Gül Deniz},
journal = {Kybernetika},
keywords = {bounded lattice; t-norm; t-conorm; ordinal sum},
language = {eng},
number = {2},
pages = {273-294},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Some methods to obtain t-norms and t-conorms on bounded lattices},
url = {http://eudml.org/doc/294262},
volume = {55},
year = {2019},
}

TY - JOUR
AU - Çaylı, Gül Deniz
TI - Some methods to obtain t-norms and t-conorms on bounded lattices
JO - Kybernetika
PY - 2019
PB - Institute of Information Theory and Automation AS CR
VL - 55
IS - 2
SP - 273
EP - 294
AB - In this study, we introduce new methods for constructing t-norms and t-conorms on a bounded lattice $L$ based on a priori given t-norm acting on $ [a,1]$ and t-conorm acting on $[0,a]$ for an arbitrary element $a\in L\backslash \lbrace 0,1\rbrace $. We provide an illustrative example to show that our construction methods differ from the known approaches and investigate the relationship between them. Furthermore, these methods are generalized by iteration to an ordinal sum construction for t-norms and t-conorms on a bounded lattice.
LA - eng
KW - bounded lattice; t-norm; t-conorm; ordinal sum
UR - http://eudml.org/doc/294262
ER -

References

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