1Department of Mathematics, Faculty of mathematics and statistics, University of Birjand, Birjand, Iran.
2Department of Mathematics, Faculty mathematics and statistics, University of Birjand, Birjand, Iran.
In this article we introduce $\mu$-filtered fuzzy module with a family of fuzzy submodules. It shows the relation between $\mu$-filtered fuzzy modules and crisp filtered modules by level sets. We investigate fuzzy topology on the $\mu$-filtered fuzzy module and apply that to introduce fuzzy completion. Finally we extend Krull's intersection theorem of fuzzy ideals by using concept $\mu$-adic completion.