Abstract
Intuitionistic fuzzy set is fruitful and more realistic model of uncertainty than the fuzzy sets. Extending this approach further, intuitionistic fuzzy soft sets were introduced, as a generalization of fuzzy soft sets and standard soft sets. Intuitionistic fuzzy soft sets used to handle the problem of muti-criteria decision making. In this paper, We initiate and establish the topological structures of intuitionistic fuzzy soft semi-open sets and intuitionistic fuzzy soft semi-closed sets. We also define and explore the properties of intuitionistic fuzzy soft semi-interior, intuitionistic fuzzy soft semi-closure and discuss the relationship between them. Moreover, we establish and discuss intuitionistic fuzzy soft semi-open neighborhood systems. We believe that the findings in this paper will enhance the further study proceed towards muti-criteria decision making problems.