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.