[PDF][PDF] Hypergroup and join space induced by a fuzzy subset
In this note by considering a fuzzy subset µ on a group G and the notion of fuzzy quotient we
first construct a hyperoperation oµ on G. We show that if µ is subnormal, then the
hyperstructure (G, oµ) is a hypergroup and under suitable conditions it is a join space. Then
we give some properties of this hyperstructure and prove some related results. Finally we
introduce the category of (fuzzy) hypergroups.
first construct a hyperoperation oµ on G. We show that if µ is subnormal, then the
hyperstructure (G, oµ) is a hypergroup and under suitable conditions it is a join space. Then
we give some properties of this hyperstructure and prove some related results. Finally we
introduce the category of (fuzzy) hypergroups.
Abstract
In this note by considering a fuzzy subset µ on a group G and the notion of fuzzy quotient we first construct a hyperoperation oµ on G. We show that if µ is subnormal, then the hyperstructure (G, oµ) is a hypergroup and under suitable conditions it is a join space. Then we give some properties of this hyperstructure and prove some related results. Finally we introduce the category of (fuzzy) hypergroups.
researchgate.net