Research on Nilpotent Groups Based on Fuzzy Hypergroups

In this paper, by constructing the smallest equivalence relation ${\theta }^{？}$ on a finite fuzzy hypergroup $H$ , the quotient group (the set of equivalence classes) $H/{\theta }^{？}$ is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of $\theta$ -part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation $\theta$ to be transitive.