Total ordering defined on the set of all intuitionistic fuzzy numbers

Abstract

L.A. Zadeh introduced the concept of fuzzy set theory as the generalisation of classical set theory in 1965 and further it has been generalised to intuitionistic fuzzy sets (IFSs) by Atanassov in 1983 to model information by the membership, non membership 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 modelled better using intutionistic fuzzy numbers introduced in [15] which generalises intuitionistic fuzzy values [1, 6, 15], interval valued intuitionistic fuzzy number (IVIFN) [9] than with usual IFNs [4, 10, 19]. 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. [9]. In this paper, a total ordering on the class of IFNs [15] using double upper dense sequence in the interval [0, 1] which generalises 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.