In this paper, we introduce filtered fuzzy module with a family of fuzzy submodules. It shows the relation between filtered fuzzy modules and crisp filtered modules by level sets. In addition, to investigate some of the characteristics of this concept, we will prove that quotient fuzzy module on a filtered fuzzy module is filtered. Finally, fuzzy version of important basic result about modules over a Noetherian ring known as Artin-Rees lemma will be expressed.

fuzzy filtered module, graded ring, associated graded ring, quotient fuzzy module, I-stable filtration, Artin-Rees lemma.