This paper defined the notion of
ω
,
θ
-complex fuzzy sets,
ω
,
θ
-complex fuzzy subgroupoid, and
ω
,
θ
-complex fuzzy subgroups and described important examples under
ω
,
θ
-complex fuzzy sets. Additionally, we discussed the conjugacy class of group with respect to
ω
,
θ
-complex fuzzy normal subgroups. We define
ω
,
θ
-complex fuzzy cosets and elaborate the certain operation of this analog to group theoretic operation. We prove that factor group with regard to
ω
,
θ
-complex fuzzy normal subgroup forms a group and establishes an ordinary homomorphism from group to its factor group with regard to
ω
,
θ
-complex fuzzy normal subgroup. Moreover, we create the
ω
,
θ
-complex fuzzy subgroup of factor group.