Abstract
The aim of this article, we combine the fuzzy soft set and fuzzy topological space. We introduce the notion of fuzzy soft set over common universe of fuzzy topological space. We defined quasi-open fuzzy soft set over fuzzy topological space and we study the properties of extended union of two quasi-open fuzzy soft set over fuzzy topological space. We study "OR" and "AND" operations of quasi-open fuzzy soft set over fuzzy topological space. We also define open fuzzy soft set, b-open fuzzy soft set and b-closed fuzzy soft set over fuzzy topological space. We give some characterizations of these concepts.