Abstract: Let Ω be a set. By combining the Ω-fuzzy sets and the lattice implication algebras, this paper introduces the concepts of Ω-fuzzy subalgebra in the lattice implication algebra, and investigates some related properties. Beside, this paper obtains some equivalent descriptions of theΩ-fuzzy subalgebra in the lattice implication algebra, and gives the relations between Ω-fuzzy subalgebra and the subalgebra in the lattice implication algebra. Then this paper studies some basic properties of theΩ-fuzzy subalgebra under the intersection, union and other operations of Ω-fuzzy sets, and discusses some basic properties of homomorphic image and homomorphic preimage of Ω-fuzzy subalgebra. Finally, this paper studies the Ω-fuzzy subalgebra direct product in the lattice implication algebra.

Key words: lattice implication algebra;Ω-fuzzy subalgebra, homomorphic, direct product

摘要： 给定一个集合Ω，将Ω-模糊集与格蕴涵代数相结合，引入了格蕴涵代数Ω-模糊子代数的概念，并研究了其相关性质；给出了格蕴涵代数Ω-模糊子代数的若干等价刻画，讨论了格蕴涵代数Ω-模糊子代数与格蕴涵代数子代数之间的相互关系；研究了格蕴涵代数Ω-模糊子代数在Ω-模糊集下交、并等运算下的基本性质；讨论了格蕴涵代数Ω-模糊子代数的同态像与同态原像的基本性质；最后研究了格蕴涵代数Ω-模糊子代数的直积与投影。

关键词: 格蕴涵代数, 模糊&Omega, -子代数, 同态, 直积