Domination in the families of Frank and Hamacher t-norms

Peter Sarkoci

Kybernetika (2005)

  • Volume: 41, Issue: 3, page [349]-360
  • ISSN: 0023-5954

Abstract

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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.

How to cite

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Sarkoci, Peter. "Domination in the families of Frank and Hamacher t-norms." Kybernetika 41.3 (2005): [349]-360. <http://eudml.org/doc/33758>.

@article{Sarkoci2005,
abstract = {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.},
author = {Sarkoci, Peter},
journal = {Kybernetika},
keywords = {domination; Frank t-norm; Hamacher $t$-norm; domination; Frank -norm; Hamacher -norm},
language = {eng},
number = {3},
pages = {[349]-360},
publisher = {Institute of Information Theory and Automation AS CR},
title = {Domination in the families of Frank and Hamacher t-norms},
url = {http://eudml.org/doc/33758},
volume = {41},
year = {2005},
}

TY - JOUR
AU - Sarkoci, Peter
TI - Domination in the families of Frank and Hamacher t-norms
JO - Kybernetika
PY - 2005
PB - Institute of Information Theory and Automation AS CR
VL - 41
IS - 3
SP - [349]
EP - 360
AB - 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.
LA - eng
KW - domination; Frank t-norm; Hamacher $t$-norm; domination; Frank -norm; Hamacher -norm
UR - http://eudml.org/doc/33758
ER -

References

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