TITLE:
Research on Nilpotent Groups Based on Fuzzy Hypergroups
AUTHORS:
Yi Yan, Yan Yan, Xinru Shang
KEYWORDS:
Fuzzy Hypergroup, Equivalence Relation, Strong Fuzzy Regular Relation, Nilpotent Group
JOURNAL NAME:
Journal of Applied Mathematics and Physics,
Vol.13 No.1,
January
16,
2025
ABSTRACT: 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
θ
to be transitive.