(α,β)-CUT of Intuitionistic Fuzzy Normed Ideals.

The main aim of this paper is to introduce the notion of (α,β)-level sets with respect to intuitionistic fuzzy normed ideals. We extend the notion of intuitionistic fuzzy normed ideals to the (α,β)-level subsets where α and β are elements in the interval[0,1]. 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 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 be obtained with the support of their (α,β)-level subsets. [ABSTRACT FROM AUTHOR]