In this work, our primary focus is to determine the intersections that exist between the family of QL-implications and the families of (S,N)- and R-implications. Toward this end, firstly, we investigate the conditions under which a QL-operation becomes a fuzzy implication. Since the exchange principle and the ordering property of fuzzy implications play an important role in this study, we propose some necessary and/or sufficient conditions on the underlying operations under which QL-operations satisfy them. As part of this attempt some interesting results pertaining to natural negations from t-conorms and the exact intersection between (S,N)- and R-implications have been obtained. We also mention some open problems relating to QL-implications.