A note on - and -Hausdorffness

In this paper, we have introduced α - and α * -Hausdorffness in an I-fuzzy topological space (in short, I-fts) in the sense of Šostak and Kubiak and characterize them in terms of the corresponding level topologies. It is shown that these notions satisfy the hereditary, productive and projective properties. The degree to which an I-fts is α - and α * -Hausdorff , is also discussed.