Some results on union of (?, ? ?qk)-fuzzy interior hyperideals of semihypergroups

In this paper, we investigate the conditions under which a given (ϵ, ϵ Vqk)-fuzzy interior hyperideal of a given semihypergroup can be realized as a union of two proper non-equivalent (ϵ, ϵ Vqk)-fuzzy interior hyperideals. Moreover, we provide a necessary and sufficient condition for the union of an arbitrary family of (ϵ, ϵ Vqk)-fuzzy interior hyperideals to be an (ϵ, ϵ Vqk)-fuzzy interior hyperideal. Finally, we discuss on the relation between the union of an arbitrary family of (ϵ, ϵ Vqk)-fuzzy interior hyperideals and the homomorphisms of semihypergroups.