Generalized fuzzy hyperideals of hyperrings

The concept of quasi-coincidence of a fuzzy interval value with an interval valued fuzzy set is considered. In fact, this is a generalized concept of the quasi-coincidence of a fuzzy point with a fuzzy set. By using this new idea, the notion of interval valued (α,β)(α,β)-fuzzy hyperideals in a hyperring is introduced and consequently, a generalization of a fuzzy hyperideal is defined. In this paper, we study the related properties of the fuzzy hyperideals and in particular, the interval valued (∈,∈∨q)(∈,∈∨q)-fuzzy hyperideals in a hyperring will be investigated. Moreover, we also consider the concept of implication-based interval valued fuzzy hyperideals in a hyperring. Some recent results obtained by B. Davvaz and J.M. Zhan on hyperstructures are extended and consolidated.