Some Results of Derivations on FI-lattices

In this paper, we further study implicative derivations on FI-lattices and obtain some new results of them. In particular, we prove that the set of all implicative derivations on FI-lattice forms a monoid. Also, we generalize the implicative derivations by homomorphism, which is called generalized implicative derivation, on FI-lattices and obtain some important results of them. The results of this paper generalize the corresponding results of derivations on the logical algebras of t-norm based fuzzy logic.