Geodesic
Domination in the families of Frank and Hamacher t-norms
Kybernetika, Tome 41 (2005) no. 3, p. [349].

Voir la notice de l'article provenant de la source Czech Digital Mathematics Library

Domination is a relation between general operations defined on a poset. The old open problem is whether domination is transitive on the set of all t-norms. In this paper we contribute partially by inspection of domination in the family of Frank and Hamacher t-norms. We show that between two different t-norms from the same family, the domination occurs iff at least one of the t-norms involved is a maximal or minimal member of the family. The immediate consequence of this observation is the transitivity of domination on both inspected families of t-norms.
Classification : 26D15
Keywords: domination; Frank t-norm; Hamacher $t$-norm 
@article{KYB_2005__41_3_a5,
     author = {Sarkoci, Peter},
     title = {Domination in the families of {Frank} and {Hamacher} t-norms},
     journal = {Kybernetika},
     pages = {[349]},
     publisher = {mathdoc},
     volume = {41},
     number = {3},
     year = {2005},
     mrnumber = {2181423},
     zbl = {1249.26041},
     language = {en},
     url = {http://geodesic.mathdoc.fr/item/KYB_2005__41_3_a5/}
}
TY  - JOUR
AU  - Sarkoci, Peter
TI  - Domination in the families of Frank and Hamacher t-norms
JO  - Kybernetika
PY  - 2005
SP  - [349]
VL  - 41
IS  - 3
PB  - mathdoc
UR  - http://geodesic.mathdoc.fr/item/KYB_2005__41_3_a5/
LA  - en
ID  - KYB_2005__41_3_a5
ER  - 
%0 Journal Article
%A Sarkoci, Peter
%T Domination in the families of Frank and Hamacher t-norms
%J Kybernetika
%D 2005
%P [349]
%V 41
%N 3
%I mathdoc
%U http://geodesic.mathdoc.fr/item/KYB_2005__41_3_a5/
%G en
%F KYB_2005__41_3_a5
Sarkoci, Peter. Domination in the families of Frank and Hamacher t-norms. Kybernetika, Tome 41 (2005) no. 3, p. [349]. http://geodesic.mathdoc.fr/item/KYB_2005__41_3_a5/