In this paper, first we define the notions of INK-algebra, INK-ideals, fuzzy sets, intuitionistic fuzzy INK-ideals and intuitionistic fuzzy closed INK-ideals. Using the concept of level subsets, we prove some theorems which show that there are some relationships between these notions. Finally we define the homomorphism of INK-algebras and then we give related theorem about the relationship between their images and intuitionistic fuzzy INK-ideals. © Published under licence by IOP Publishing Ltd.