In the present paper, we introduced topological notions defined by means of regular open sets when these are planted into the framework of Ying’s
fuzzifying topological spaces (in Lukasiewicz fuzzy logic). We used fuzzy logic to introduce almost separation axioms T0R-; T1R-; T2R(almost Hausdorff)-, T3R (almost regular)- and T4R (almost-normal). Furthermore, the R0Rand  R1R-separation axioms have been studied and their relations with the T1R- and T2R-separation axioms have been introduced. Moreover, we gave the relations of these axioms with each other as well as the relations with other fuzzifying separation axioms.

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