In this paper, first we define the notation of INK-algebra-ideal, fuzzy set, intuitionistic fuzzy K-ideals and intuitionistic fuzzy closed K-ideals,direct product of intuitionistic fuzzy K-ideals in INK-algebras .Using the concept of level subset, we prove some theorems which show that there are some relationships between these notation. Finally we define the homomorphism of INK-algebra and then we give related theorem about the relationship between their images and direct product of intuitionistic fuzzy K-ideals. © 2019 Elsevier Ltd. All rights reserved. Selection and/or Peer-review under responsibility of International Conference on Advances in Materials, Manufacturing and Applied Sciences.