On a new class of implications: (g,u)-implications and the distributive equations

•We introduced a new class of implications called (g,u)-implications which is also a generalization of Yager’s g-implication.•We discussed some properties and characterized this new class of implications.•The distributive equations of this new class of implications are investigated.

In this paper, Yager’s g-implications are generalized, and a new class of implications, called (g,u)-implications, is introduced. It is shown that (g,u)-implications are not only the generalization of Yager’s g-implications, but also the generalization of (S,N)-, R-, QL-implications. Basic properties and characterization of these implications are discussed. Furthermore, the distributive equations of these implications are investigated.