On the Fuzzy Subhypergroups of Some Particular Complete Hypergroups (I)

Any complete hypergroup H may be represented as the union g gG HA ∈ =  , where G is a group and the subsets Ag of H satisfy certain properties. With any hypergroupoid 〈H, o〉 we may associate a particular fuzzy set µ . In this paper we determine sufficient and necessary conditions for a finite complete hypergroup 〈H, o〉, where p G( Z,) ≅+ or 2p G( Z, ) ≅+ , p a prime number, such that the fuzzy set µ is a fuzzy subhypergroup of H. Moreover, as an intermediate result, we give a new decomposition of the multiplicative group Zp\{0}, with p an odd prime.