Abstract: Fuzzy homomorphism is based on fuzzy mapping，fuzzy homomorphism of group and ring is discussed by different fuzzy mapping respectively.The concepts of fuzzy homomorphism and fuzzy weak homomorphism of lattice are introduced by fuzzy mapping of the classical sets.Some correspondence relations among fuzzy sub-lattices（fuzzy ideals） under fuzzy homomorphism and fuzzy weak homomorphism are obtained.The ideal of lattice is gained and the isomorphism among lattices is established by use of the fuzzy homomorphism.At last，based on mapping under fuzzy homomorphism，the weak homomorphism（epimorphism） of fuzzy sub-lattices is studied.

Key words: fuzzy mapping, fuzzy homomorphism, fuzzy weak homomorphism

摘要： 研究模糊同态，自然离不开模糊映射，群与环的模糊同态分别利用了不同的模糊映射进行讨论。利用经典集间的模糊映射，引入了格的模糊同态和模糊弱同态概念，给出了模糊同态与模糊弱同态下模糊子格（模糊理想）的对应关系，并由模糊同态得到了格的理想，建立了格的同构映射，基于模糊同态所确定的映射等价刻画了模糊子格的弱（满）同态。

关键词: 模糊映射, 模糊同态, 模糊弱同态