In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characteriz...In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.展开更多
文摘In this paper, by constructing the smallest equivalence relation θ∗on a finite fuzzy hypergroup H, the quotient group (the set of equivalence classes) H/θ∗is a nilpotent group, and the nilpotent group is characterized by the strong fuzzy regularity of the equivalence relation. Finally, the concept of θ-part of fuzzy hypergroup is introduced to determine the necessary and sufficient condition for the equivalence relation θto be transitive.
