QL-implications on a finite chain

This paper deals with a kind of implications defined from t-norms, t-conorms and strong negations on a finite chain, through the expression I(x,y) = S(N(x),T (x,y)), and called QL-implications. We mainly study those QL-implications derived from smooth t-norms and t-conorms. It is characterized when functions defined in this way are implication functions, and their analytical expression is given. Some additional properties are studied like contrapositive symmetry, the exchange principle and others. In particular, it is proved that a QL-implication satisfies the exchange principle if and only if it is also an S-implication. Finally, some QL-implications are also derived from non smooth t-norms or t-conorms.