The aim of this paper is to introduce a new concept of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals on ternary semigroups. We extend the concept of fuzzy bi-ideals and fuzzy interior ideals to the context of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals, respectively. Some characterizations of hesitant fuzzy bi-ideals and hesitant fuzzy interior ideals are obtained. Moreover, we investigate relationships between hesitant fuzzy ideals and hesitant fuzzy interior ideals on ternary semigroups. Finally, we obtain necessary and sufficient conditions of hesitant fuzzy interior ideal in order to be a hesitant fuzzy ideal.