Equivalence among some neighborhood structures in fuzzy topology

We deepen the study of two known neighborhood structures, which here will be called f · k-neighborhood structures and f · q-neighborhood structures, in the context of Šostak fuzzy topological spaces. In particular, we characterize fuzzy topologies by f · k-neighborhood structures. Moreover we introduce and discuss the notions of f · kneighborhood prestructure and f ·m-neighborhood structure in the same context. At last we prove that the three neighborhood structures mentioned above are equivalent.