Abstract
In this paper, we introduce and study a new sort of fuzzy n-ary sub-hypergroups of an n-ary hypergroup, called $$(\in,\in \vee q)$$-fuzzy n-ary sub-hypergroup. By using this new idea, we consider the $$(\in,\in\vee q)$$-fuzzy n-ary sub-hypergroup of a n-ary hypergroup. This newly defined $$(\in,\in \vee q)$$-fuzzy n-ary sub-hypergroup is a generalization of the usual fuzzy n-ary sub-hypergroup. Finally, we consider the concept of implication-based fuzzy n-ary sub-hypergroup in an n-ary hypergroup and discuss the relations between them, in particular, the implication operators in $$\pounds$$ukasiewicz system of continuous-valued logic are discussed.
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