A fuzzy subset f of an ordered groupoid (or groupoid) S is called fuzzy semiprime if f (x) ≥ f (x 2) for every x ∈ S; it is called fuzzy prime if f (xy) ≤ min{ f (x), f (y)} for every x, y ∈ S (Definition 1). Following the terminology of semiprime subsets of ordered groupoids (or groupoids) and the terminology of ideal elements of poe-groupoids (: ordered groupoids possessing a greatest element), a fuzzy subset f of an ordered groupoid (or groupoid) should be called fuzzy semiprime if for every fuzzy subset of S such that 2 := • f , we have f ; it should be called prime if for any fuzzy subsets h, of S such that h • f we have h f of f (Definition 2). And this is because if S is a groupoid or an ordered groupoid, then the set of all fuzzy subsets of S is a poe-groupoid. What is the relation between these two definitions? that is between the Definition 1 (the usual definition we always use) and the Definition 2 given in this paper? The present paper gives the related answer.