Due to importance of the concepts of θ-closure and δ-closure, it is natural to try for their extensions to fuzzy topological spaces. So, Ganguly and Saha introduced and investigated the concept of fuzzy δ-closure by using the concept of quasicoincidence in fuzzy topological spaces. In this paper, we will introduce the concept of δ-closure in intuitionistic fuzzy topological spaces, which is a generalization of the δ-closure by Ganguly and Saha.

In this paper, we characterize the intuitionistic fuzzy δ-continuous, intuitionistic fuzzy weakly δ-continuous, intuitionistic fuzzy almost continuous, and intuitionistic fuzzy almost strongly θ-continuous functions in terms of intuitionistic fuzzy δ-closure and interior or θ-closure and interior.

In this paper, we introduce certain types of continuous functions and intuitionistic fuzzy θ-compactness in intuitionistic fuzzy topological spaces. We show that intuitionistic fuzzy θ-compactness is strictly weaker than intuitionistic fuzzy compactness. Furthermore, we show that if a topological space is intuitionistic fuzzy retopologized, then intuitionistic fuzzy compactness in the new intuitionistic fuzzy topology is equivalent to intuitionistic fuzzy θ-compactness in the original intuitionistic fuzzy topology. This characterization shows that intuitionistic fuzzy θ-compactness can be related to an appropriated notion of intuitionistic fuzzy convergence.

In our previous paper, we proposed a new definition of intuitionistic fuzzy rough sets. In this paper, we propose a topology for redefined intuitionistic fuzzy rough sets and investigate the basic properties of their subspaces, transition spaces, and continuous functions. Moreover, we obtain the adjointness between the categories of fuzzy rough sets and intuitionistic fuzzy rough sets. The results obtained from this new definition differ from those of previous studies.