This article gives results on fixed complete lattice L -fuzzy pre-proximities, L -fuzzy grills and L -fuzzy filters. Moreover, we investigate the relations among the L -fuzzy pre-proximities , L -fuzzy grills and L -fuzzy filters. We show that there is a Galois correspondence between the category of separated L -fuzzy grill spaces and that of separated L -fuzzy pre-proximity spaces. We introduced the local function associated with L -fuzzy grill and L -fuzzy topology and studied some of its properties. Finally, we build an L -fuzzy topology for the corresponding L -fuzzy grill by using local function.

中文翻译：

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L-fuzzy pre-proximities、L-fuzzy 过滤器和 L-fuzzy 格栅

这篇文章给出了固定完全格子 L -fuzzy pre-proximities、L -fuzzy grids 和 L -fuzzy filter 的结果。此外，我们研究了 L-fuzzy pre-proximities、L-fuzzy 格栅和 L-fuzzy 过滤器之间的关系。我们表明分离的 L -模糊格栅空间的类别与分离的 L -模糊前邻近空间的类别之间存在伽罗瓦对应。我们介绍了与 L -模糊格栅和 L -模糊拓扑相关的局部函数并研究了它的一些性质。最后，我们通过使用局部函数为相应的 L -模糊格栅构建 L -模糊拓扑。