Affiliations: [a] Department of Mathematics, Faculty of Science, Assiut University, Assiut, Egypt
| [b] Department of Mathematics, Faculty of Science, New Valley University, Egypt
| [c] School of Mathematics and Statistics, Qinghai Normal University, Xining, P. R. China
Correspondence:
[*]
Corresponding author. Gui-Xiu Chen, School of Mathematics and Statistics, Qinghai Normal University, 810008, Xining, P. R. China. E-mail: chenguixiu@qhnu.edu.cn.
Abstract: In the present paper, a characterization of the intuitionistic fuzzy sets, the interval-valued intuitionistic fuzzy sets and their set-operations are given. By making use of these characterizations, the relationships between the interval-valued intuitionistic fuzzy topology and four fuzzy topologies associated to it are studied. For this reason, some subclasses of the family of interval-valued intuitionistic fuzzy topologies on a set which we call pre-suitable and suitable are introduced. Furthermore, the concepts of homeomorphism functions and compactness in the framework of interval-valued intuitionistic fuzzy topological spaces are introduced and studied.
