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