As a generalization of the concept of an interval-valued fuzzy bi-ideal (respectively, subsemigroup, generalized bi-ideal, left ideal, right ideal) of a semigroup, the concept of a sup-hesitant fuzzy bi-ideal (respectively, subsemigroup, generalized bi-ideal, left ideal, right ideal) is introduced, investigated some properties and discussed the generalizations of these hesitant fuzzy sets. We characterize  sup-hesitant fuzzy subsemigroups, sup-hesitant fuzzy left (right) ideals, sup-hesitant fuzzy  (generalized) bi-ideals and  sup-hesitant fuzzy (interior) ideals in terms of level sets,  fuzzy sets, Pythagorean fuzzy sets,  interval-valued fuzzy sets, cubic sets,  hesitant fuzzy sets and hybrid sets. Moreover, subsemigroups, (generalized) bi-ideals, and left (right) ideals of semigroups are characterized by sup-types of hesitant fuzzy sets.