Abstract
In this paper, we introduce the largest family of generalized fuzzy subhypergroups based on concepts of belongingness and quasi-coincidence of a fuzzy point to a fuzzy subset. In this regards, $$(\in ,\in \vee q^{\delta })$$-fuzzy subhypergroups and $$(\in ,\in \vee q^{\delta }_{k})$$-fuzzy subhypergroups of hypergroups are defined as a generalization of fuzzy subhypergroups, $$(\in , \in \vee q)$$-fuzzy subhypergroups and $$(\in , \in \vee q_{k})$$-fuzzy subhypergroups of hypergroups. Some properties of them are investigated and their differences with other types are studied.
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