Intersection of Yager's implications with QL and D-implications (Q448930)

The \(f\)- and \(g\)-generated implications were introduced by \textit{R. R. Yager} [Inf. Sci. 167, No. 1--4, 193--216 (2004; Zbl 1095.68119)]. In this article the authors deal with characterizations of intersections of Yager's implications with other well-known families of fuzzy implication functions. Firstly, the authors solve an open problem related to the characterization of those implications that are both QL-implications and \(f\)-generated implications with \(f(0) < \infty\). Next, the authors perform a similar study for D-implications, and finally they study the intersection of Yager's implications with their \(\varphi \)-conjugates. Some interesting notes on the intersection of Yager's implications with (S, N)- and R-implications are also included in the paper.