  L.A.Zadeh introduced the concept of fuzzy set theory as the generalization of
classical set theory in 1965 and further it has been generalized to
intuitionistic fuzzy sets (IFSs) by Atanassov in 1983 to model information by
the membership, nonmembership and hesitancy degree more accurately than the
theory of fuzzy logic. The notions of intuitionistic fuzzy numbers in different
contexts were studied in literature and applied in real life applications.
Problems in different fields involving qualitative, quantitative and uncertain
information can be modeled better using intutionistic fuzzy numbers introduced
in [17] which generalizes intuitionistic fuzzy values [1,7,17], interval valued
intuitionistic fuzzy number (IVIFN) [10] than with usual IFNs [5,11,21].
Ranking of fuzzy numbers have started in early seventies in the last century
and a complete ranking on the class of fuzzy numbers have achieved by W.Wang
and Z.Wang only on 2014. A complete ranking on the class of IVIFNs, using
axiomatic set of membership, non membership, vague and precise score functions
has been introduced and studied by Geetha et al.[10]. In this paper, a total
ordering on the class of IFNs [17] using double upper dense sequence in the
interval [0; 1] which generalizes the total ordering on fuzzy numbers (FNs) is
proposed and illustrated with examples. Examples are given to show the proposed
method on this type of IFN is better than existing methods and this paper will
give the better understanding over this new type of IFNs.
