t-Norm based cuts of intuitionistic fuzzy sets

We consider the system of intuitionistic fuzzy sets (IF-sets) in a universe X and study the cuts of an IF-set. Suppose a left continuous triangular norm is given. The t-norm based cut (level set) of an IF-set is defined in a way that binds the membership and nonmembership functions via the triangular norm. This is an extension of usual cuts of IF-sets. We show that the system of these cuts fulfils analogical properties as usual systems of cuts. However, it is not possible to reconstruct an IF-set from the system of t-norm based cuts.