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.
['Margarita Mas', 'Miquel Monserrat', 'Joan Torrens']
S-implications and R-implications on a finite chain