中文摘要：

以交换单位quantale为取值格,研究了模糊完备格上的模糊G-理想。首先,给出了模糊G-理想的定义,证明了由X×Y上的所有模糊G-理想构成的集合在包含度下是一个模糊完备格。其次,研究了模糊G-理想和模糊Galois伴随之间的关系,证明了由X×Y上的模糊G-理想构成的模糊完备格与X和Y之间的模糊Galois伴随构成的模糊完备格相互同构。

英文摘要：

This paper deals with fuzzy G-ideals on fuzzy complete lattices. Firstly,the concept of fuzzy G-ideals is defined and it is proved that the set of all fuzzy G-ideals of X × Y is a fuzzy complete lattice with respect to fuzzy in clusion order. Secondly,by making use of the intrinsic fuzzy inclusion orders on fuzzy G-ideals,the relationship between fuzzy Galois connections and fuzzy G-ideals is studied. It is shown that the fuzzy poset of fuzzy Galois connections between fuzzy complete lattices X and Y is order-isomorphic to the fuzzy poset of all fuzzy G-ideals of X × Y.