Abstract
In this paper, by means of a kind of new idea, we consider the ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$ -hyperrings. The notion of ( ∈ , ∈ ∨ q)-fuzzy hyperideals of $$\Upgamma$$ -hyperrings is provided and some related properties are investigated. A kind of quotient $$\Upgamma$$ -hyperring of a $$\Upgamma$$ -hyperring by an ( ∈ , ∈ ∨ q)-fuzzy hyperideal is presented and the relationships among ( ∈ , ∈ ∨ q)-fuzzy hyperideals, quotient $$\Upgamma$$ -hyperrings and homomorphisms are explored. Several homomorphism theorems in the framework of fuzzy setting are provided.
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