Abstract: The concepts of θ-fuzzy mapping and θ-fuzzy homomorphism of groups are introduced. Some properties of the θ-fuzzy homomorphism are studied, and the relationships between the (λ, μ)-fuzzy normal subgroups under θ-fuzzy homomorphism are discussed. Finally, the fundamental theorem of θfuzzy homomorphism is established.

Key words: θ-fuzzy mapping, (λ, μ)-fuzzy normal subgroup, θ-fuzzy homomorphism