R. A Borzooei - Department of Mathematics, Shahid Beheshti University, Tehran, Iran
M Sabet Kish - Department of Mathematics, Shahid Beheshti University, Tehran, Iran

In this paper, we introduce the notion of intuitionistic fuzzy implicative filter and find equivalent conditions, and therelated results are investigated. The relation between intuitionistic fuzzy filter and intuitionistic fuzzy implicative filteris discussed. Finally, we introduce a congruence relation by using intuitionistic fuzzy filter and we show that the inducedquotient structure is a lattice implication algebra. Its structure and properties have been studied extensively by manyresearchers. In the paper, based on the concept of lattice implication algebra and the properties of the implicative filter,and combining the concept and properties of the intuitionistic fuzzy set, the intuitionistic fuzzy implicative filter inlattice implication algebra is defined.

lattice implication algebra, fuzzy set, intuitionistic fuzzy set, filter, implicative filter