Abstract: By using the method and principle of fuzzy sets, the concept of n-fold fuzzy implicative filter, n-fold fuzzy fantastic filter, n-fold fuzzy positive implicative filter and n-fold fuzzy Boole filter were introduced in residuated lattice. The author obtained the relation among these kinds of n-fold fuzzy filter in residuated lattice, and proved that the equivalence between n-fold fuzzy positive implicative filter and n-fold fuzzy Boole filter in residuated lattice.

Key words: n-fold fuzzy positive implicative filter, n-fold fuzzy implicative filter, n-fold fuzzy Boole filter, n-fold fuzzy fantastic filter, residuated lattice