Abstract
In this paper, we defined the notions of $(\in,\in)$ -fuzzy implicative deductive systems and $(\in,\in\vee q)$ -fuzzy implicative deductive systems of hoops and studied some traits and tried to define some definitions that are equivalent to them. Thus by using the notion of $(\in,\in)$ -fuzzy deductive system of hoop, we defined a new congruence relation on hoop and show that the algebraic structure that is made by it is a Brouwerian semilattice , Heyting algebra and Wajesberg hoop.
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