(2006-1007) Some types of derivations in bounded commutative residuated lattices

In this paper, the notion of mutiplicative derivation, pseudo implicative derivation and implicative derivation on a bounded commutative residuated lattice are presented with some useful examples. We generalized these notions of derivation by introducing (f, g)-multiplicative derivation, (f, g)-pseudo implicative derivation and (f, g)-implicative derivation, and discussed some related properties; the conditions for (f, g)-multiplicative derivation, (f, g)-pseudo implicative derivation and (f, g)-implicative derivation to be monotone are provided. The set of fixed points is defined by using the notion of (f, g)-multiplicative derivation of bounded commutative residuated lattices. We also analyzed the link between different types of derivation.