We have often seen in the bibliography that "fuzzy semigroups were introduced as a generalization of classical semigroups". What does it mean~? In this paper we prove that every groupoid (resp. semigroup) $(S, .)$ is embedded in the groupoid (resp. semigroup) of all fuzzy subsets of $S$. In addition, the set of all fuzzy subsets of a groupoid (resp. semigroup) $S$ is a $poe$-groupoid (resp. $poe$-semigroup) having a zero element. As a consequence, every groupoid (resp. semigroup) $S$ is embedded into a $poe$-groupoid (resp. $poe$-semigroup) having a zero element.