In this paper, we study the concept of weak linear fuzzy topology on a topological vector space as generalization usual topology. We prove that consists all weakly lower semi-continuous sets given when K (R or C) endowed with its case is different from topology, show not equivalent sets.

We study FTOP (L), a fuzzy category related to topology with fuzzy functions in the role of morphisms.

In this article we introduce μ-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between μ-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the μ-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull’s intersection theorem of fuzzy ideals by using concept μ-adic completion.