In this paper, as a generalization of the concepts of hesitant fuzzy bi-ideals and hesitant fuzzy right (resp. left) ideals of semigroups, the concepts of hesitant fuzzy
m
,
n
-ideals and hesitant fuzzy
m
,
0
-ideals (resp.
0
,
n
-ideals) are introduced. Furthermore, conditions for a hesitant fuzzy
m
,
n
-ideal (
m
,
0
-ideal,
0
,
n
-ideal) to be a hesitant fuzzy bi-ideal (right ideal, left ideal) are provided. Moreover, several correspondences between bi-ideals (right ideals, left ideals) and hesitant fuzzy
m
,
n
-ideals (
m
,
0
-ideals,
0
,
n
-ideals) are obtained. Also, the characterizations of different classes of semigroups in terms of their hesitant fuzzy
m
,
n
-ideals and hesitant fuzzy
m
,
0
-ideals (
0
,
n
-ideals) are investigated.