Abstract
In the present paper, we introduce the notions of r-fuzzy star-open and r-fuzzy star-closed sets in Sostak's fuzzy topological spaces. Also, we study some properties of these notions. Moreover, we give the concept of fuzzy ideal star-irresolute mapping in Sostak's fuzzy topological spaces. Finally, we study some kinds of separation axioms namely r - FIRi where i={0.1.2.3} and r - FITj where j={1.2.21/2.3.4} and the relations between them. Also, some of their characterizations and several of fundamental properties have been established. (C) 2020 The Authors. Published by IASE.