In t-norm-based fuzzy logics there are different ways to introduce implication operators. Most common is the reference to a residuation operation similar to intuitionistic logic, yielding the R-implications. A definition via reference to the classically equivalent formula \(\neg p \lor q\) yields S-implications depending upon a t-conorm and a negation function. Similarly, the QL-implications are defined via reference to the classically equivalent formula \(\neg p \lor (p\land q)\) and hence depend upon a t-norm, a t-conorm, and a negation function. The authors study this last class of implication operators. First, they discuss how properties of QL-implications depend upon properties of their defining functions. And second, they compare the class of QL-implications with the classes of the R-implications and the S-implications.