In the present paper, we introduce topological notions defined by means
of α-open sets when these are planted into the framework of Ying’s
fuzzifying topological spaces (by Lukasiewicz logic in [0, 1]). We introduce T 0 α -; T 1 α -; T 2 α  (α- Hausdorff)-, T 3 α  (α-regular)- and T 4 α  (α-normal)-separation axioms. Furthermore, the R 1 α - and R 2 α -separation axioms are studied and their relations with the T 1 α - and T 2 α -separation axioms are introduced. Moreover, we clarify the relations of these axioms with each other as well as the relations with other
fuzzifying separation axioms.