Algebraic Properties of ω , θ -Complex Fuzzy Subgroups

Abstract

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