Geodesic
Some methods to obtain t-norms and t-conorms on bounded lattices
Kybernetika, Tome 55 (2019) no. 2, pp. 273-294 Cet article a éte moissonné depuis la source Czech Digital Mathematics Library

Voir la notice de l'article

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 $a\in L\backslash \{0,1\}$. 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.
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 $a\in L\backslash \{0,1\}$. 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.
DOI : 10.14736/kyb-2019-2-0273
Classification : 03B52, 03E72, 06B20, 94D05, 97E30
Keywords: bounded lattice; t-norm; t-conorm; ordinal sum 
@article{10_14736_kyb_2019_2_0273,
     author = {\c{C}ayl{\i}, G\"ul Deniz},
     title = {Some methods to obtain t-norms and t-conorms on bounded lattices},
     journal = {Kybernetika},
     pages = {273--294},
     year = {2019},
     volume = {55},
     number = {2},
     doi = {10.14736/kyb-2019-2-0273},
     mrnumber = {4014587},
     zbl = {07144938},
     language = {en},
     url = {http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-2-0273/}
}
TY  - JOUR
AU  - Çaylı, Gül Deniz
TI  - Some methods to obtain t-norms and t-conorms on bounded lattices
JO  - Kybernetika
PY  - 2019
SP  - 273
EP  - 294
VL  - 55
IS  - 2
UR  - http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-2-0273/
DO  - 10.14736/kyb-2019-2-0273
LA  - en
ID  - 10_14736_kyb_2019_2_0273
ER  - 
%0 Journal Article
%A Çaylı, Gül Deniz
%T Some methods to obtain t-norms and t-conorms on bounded lattices
%J Kybernetika
%D 2019
%P 273-294
%V 55
%N 2
%U http://geodesic.mathdoc.fr/articles/10.14736/kyb-2019-2-0273/
%R 10.14736/kyb-2019-2-0273
%G en
%F 10_14736_kyb_2019_2_0273
Çaylı, Gül Deniz. Some methods to obtain t-norms and t-conorms on bounded lattices. Kybernetika, Tome 55 (2019) no. 2, pp. 273-294. doi: 10.14736/kyb-2019-2-0273

Cité par Sources :