Types of (f,g)-derivations in residuated lattices

In this paper, we introduce three types of (f, g)-derivations suchas one, two and three (f, g)-derivations of residuated lattices and investigate someproperties of them. Then we show that if d is a (f, g)- derivation preserving, thend is isotone. We prove a formula for n-th (f, g)-derivations of type one. Finally,we show that the set of all (f, g)-derivation preserving ⊙ on residuated lattices, isa semi- group.