Abstract

Abstract In this paper, by means of a new idea, the concept of (invertible) (∈,∈∨q)-fuzzy n-ary subhypergroups of a commutative n-ary hypergroup is introduced and some related properties are investigated. A kind of n-ary quotient hypergroup by an (∈, ∈∨q)-fuzzy n-ary subhypergroup is provided and the relationships among (∈, ∈∨q)-fuzzy n-ary subhypergroups, n-ary quotient hypergroups and homomorphism are investigated. Several isomorphism theories of n-ary hypergroups are established.

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