Constructing a Heyting Semilattice that has Wajesberg Property by Using Fuzzy Implicative Deductive Systems of Hoops

Abstract

In this paper, we defined the notions of (is an element of, is an element of)-fuzzy implicative deductive systems and (is an element of, is an element of boolean OR 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 (is an element of, is an element of)-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.