creative_2024_33_1_119_128P. S. Das [Sivaramakrishna Das, P. Fuzzy groups and level subgroups. J. Math. Anal. Appl. 84 (1981), no. 1, 264–269.] proved that the level subgroups of any fuzzy subgroup of a finite group form a chain. In this paper we extend it to modules and showed that the level submodules of a fuzzy module also form a chain. With the help of these results we introduced fuzzy noetherian module for noetherian modules. Some results are proved for level submodules of any fuzzy module of modules with composition series.
