Geodesic
S-implications and $R$-implications on a finite chain
Kybernetika, Tome 40 (2004) no. 1, p. [3].

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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.
Classification : 03B52, 06F05, 94D05
Keywords: t-norm; T-conorm; finite chain; smoothness; implication operator 
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Mas, Margarita; Monserrat, Miquel; Torrens, Joan. S-implications and $R$-implications on a finite chain. Kybernetika, Tome 40 (2004) no. 1, p. [3]. http://geodesic.mathdoc.fr/item/KYB_2004__40_1_a1/