Constructing a Heyting semilattice that has Wajesberg property by using fuzzy implicative deductive systems of Hoops

M. M. Aaly Kologani, X.L. Xin, M. Mohseni Takallo, Y.B. Jun, Rajab Ali Borzooei

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.

Keywords


Hoop, fuzzy implicative deductive system, Brouwerian semilattice, Heyting algebra, Wajesberg hoop.

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