Abstract: Extended the notion of lattice H implication algebra L under a norm situation （i. e. , normed lattice H implication algebras）, and some properties were discussed. At the other hand, by applying the fuzzy set concept to normed lattice H implication algebra

Key words: Normecl lattice H implication algebra, Fuzzy normed lattice H implication algebra, Lattice H implication homomorphism, Sequence