This paper aims to define fuzzy pretopogenous structure based on way below relation (or an L-fuzzifying pretopogenous structure (LFPT structure, for short)) and study some of its properties. Also, the concepts of L-fuzzifying pre-neighborhood, L-fuzzifying pre-interior, and L-fuzzifying pre-closure operators are established and we used these concepts to build an L-fuzzifying topology. Furthermore, a natural link is established between L-fuzzifying pretopogenous and L-fuzzifying topology. Finally, the maps between L-fuzzifying pretopogenous structures and initial fuzzifying structures are investigated.