We propose in this work a novel idea to construct a kind of fuzzy soft topological space via utilizing the definition of Binary Relation-FS-set, which was presented recently, and it is called Binary Relation-FS-topological spaces. We center around the foundational definitions and main properties of the Binary Relation-FS-topology, such as, the Binary Relation -FS-interior, and Binary Relation -FS-closure, with some basic theorems. This new kind of fuzzy-soft topology is more functional and advantageous, and it also contributes to some scientific applications. Furthermore, an advantageous and important applied example is presented.