Nour Abed Alhaleem - Universiti Kebangsaan Malaysia,UKM Bangi, Selangor, Malaysia.
Abd Ghafur Ahmad - Universiti Kebangsaan Malaysia,UKM Bangi, Selangor, Malaysia.

In this paper, the (α,β)-level sets where α and β are elements in the interval [۰,۱] is introduced. Several related properties for (α,β)-cut of intuitionistic fuzzy normed ideals in a normed ring (NR) will be studied and proven. Further, for any two normed rings NR,NR^' with a mapping f:NR → NR^', a relation between the intuitionistic fuzzy normed ideal I of NR and the intuitionistic fuzzy normed ideal f(I) (the image of I) of NR^' will been obtained with the support of their (α,β)-level subsets.

Intuitionistic fuzzy normed ideals, Level sets, (α, β)-cut, homomorphisms