Abstract
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.
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