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

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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 
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     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/}
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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/