In 2001, Turunen  proposed the notions of implicative filters and Boolean filters (Boolean deductive systems) and proved that implicative filters are equivalent to Boolean filters in BL-algebras. Boolean filters are important filters, because the quotient algebras induced by Boolean filters are Boolean algebras. Jun and Ahn  provided several degrees in defining a fuzzy implicative filter. Meng  introduced the concept of implicative ideals in BCK-algebras and investigated the relationship of it with the concepts of positive implicative ideals and commutative ideals. Meng et al.  and Mostafa  fuzzified the concept of implicative ideals in BCK-algebras independently. Also, Xu and Qin  proposed the notions of implicative filters and fuzzy implicative filters of lattice implication algebras.