中文摘要：

利用L-模糊集内积的概念分别给出了由L-模糊关系、反身、对称的L-模糊关系生成的L-模糊上近似的唯一公理刻画。

英文摘要：

By the notion of inner products of L-fuzzy sets, this paper uses only one axiom to describe the upper approximation generated by the L-fuzzy relations, the reflexive and symmetric L-fuzzy relations, respectively.