S-implications and R -implications on a finite chain

Margarita Mas; Miquel Monserrat; Joan Torrens

Kybernetika (2004)

  • Volume: 40, Issue: 1, page [3]-20
  • ISSN: 0023-5954

Abstract

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This paper is devoted to the study of two kinds of implications on a finite chain L : S -implications and R -implications. A characterization of each kind of these operators is given and a lot of different implications on L are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class satisfies that both, its S -implication and its R -implication, agree.

How to cite

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Mas, Margarita, Monserrat, Miquel, and Torrens, Joan. "S-implications and $R$-implications on a finite chain." Kybernetika 40.1 (2004): [3]-20. <http://eudml.org/doc/33682>.

@article{Mas2004,
abstract = {This paper is devoted to the study of two kinds of implications on a finite chain $L$: $S$-implications and $R$-implications. A characterization of each kind of these operators is given and a lot of different implications on $L$ are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class satisfies that both, its $S$-implication and its $R$-implication, agree.},
author = {Mas, Margarita, Monserrat, Miquel, Torrens, Joan},
journal = {Kybernetika},
keywords = {t-norm; T-conorm; finite chain; smoothness; implication operator; -norm; -conorm; finite chain; smoothness; implication operator},
language = {eng},
number = {1},
pages = {[3]-20},
publisher = {Institute of Information Theory and Automation AS CR},
title = {S-implications and $R$-implications on a finite chain},
url = {http://eudml.org/doc/33682},
volume = {40},
year = {2004},
}

TY - JOUR
AU - Mas, Margarita
AU - Monserrat, Miquel
AU - Torrens, Joan
TI - S-implications and $R$-implications on a finite chain
JO - Kybernetika
PY - 2004
PB - Institute of Information Theory and Automation AS CR
VL - 40
IS - 1
SP - [3]
EP - 20
AB - This paper is devoted to the study of two kinds of implications on a finite chain $L$: $S$-implications and $R$-implications. A characterization of each kind of these operators is given and a lot of different implications on $L$ are obtained, not only from smooth t-norms but also from non smooth ones. Some additional properties on these implications are studied specially in the smooth case. Finally, a class of non smooth t-norms including the nilpotent minimum is characterized. Any t-norm in this class satisfies that both, its $S$-implication and its $R$-implication, agree.
LA - eng
KW - t-norm; T-conorm; finite chain; smoothness; implication operator; -norm; -conorm; finite chain; smoothness; implication operator
UR - http://eudml.org/doc/33682
ER -

References

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