The notion of a fuzzy upper bound over a groupoid is introduced and some properties of it are investigated. We also define the notions of an either-or subset of a groupoid and a strong either-or subset of a groupoid and study some of their related properties. In particular, we consider fuzzy upper bounds in Bin(X), where Bin(X) is the collection of all groupoids. Finally, we define a fuzzy-d-subset of a groupoid and investigate some of its properties.