As a generalization of fuzzy subsemigroups, the notion of ${varepsilon}$-generalized fuzzy subsemigroups is introduced, and several properties are investigated. A condition for an ${varepsilon}$-generalized fuzzy subsemigroup to be a fuzzy subsemigroup is considered. Characterizations of ${varepsilon}$-generalized fuzzy subsemigroups are established, and we show that the intersection of two ${varepsilon}$-generalized fuzzy subsemigroups is also an ${varepsilon}$-generalized fuzzy subsemigroup. A condition for an ${varepsilon}$-generalized fuzzy subsemigroup to be ${varepsilon}$-fuzzy idempotent is discussed. Using a given ${varepsilon}$-generalized fuzzy subsemigroup, a new ${varepsilon}$-generalized fuzzy subsemigroup is constructed. Finally, the fuzzy extension of an ${varepsilon}$-generalized fuzzy subsemigroup is considered.