In this paper, we show that any stratified L -topological group G, is uniformizable. That is, we define, using the family of prefilters which corresponds the fuzzy neighborhood filter at the identity element of G,, unique left and right invariant fuzzy uniform structures on G compatible with the fuzzy topology . On the other hand, on any group G , using a family of prefilters on G fulfills certain conditions, we construct those left and right fuzzy uniform structures which induce a stratified fuzzy topology  on G for which G, is a stratified L -topological group and this family of prefilters coincides with the family of prefilters corresponding to the fuzzy neighborhood filter at the identity element of G,. Moreover, we show the relation between the L topological groups and the GTi -spaces, such as: the fuzzy topology of an L -topological group (resp., a separated L -topological group) is completely regular, (resp., )