Intersection of Yager’s implications with QL and D-implications

The intersection of the different classes of implications is one of the most popular topics nowadays due to the large number of construction methods of these operators. In this paper, we deal with the characterization of the intersection of Yager’s implications with QL and D-implications. Some initial steps have already been made with the intersection of Yager’s implications with (S, N), R and QL-implications, however some questions remain unanswered. In particular, we solve an open problem related to the characterization of those implications that are both QL-implications and f-generated implications with f(0) < ∞, fully determining the expression of the QL-implications generated by a continuous t-conorm that belong to the considered intersection. Furthermore, we perform a similar study for D-implications and finally, we study the intersection of Yager’s implications with their φ-conjugates.