An approach to fuzzy frames via fuzzy posets

In this paper, based on a complete Heyting algebra L, we define a fuzzy version of frames, called L- frames. Then we construct an adjunction between the category of stratified L- topological spaces and that of L- locales (the opposite category of L- frames), which is a fuzzy counterpart of the Isbell-adjunction between topological spaces and locales. We also study the corresponding sobriety of stratified L- topologies and spatiality of L- frames and show the dual equivalence between them.