Relative-distance-based approaches for ranking intuitionistic fuzzy values

During the uncertain information processing on Atanassov’s intuitionistic fuzzy sets, the ranking for intuitionistic fuzzy values (IFVs) is an important and omnipresent issue. Even though many orders used to compare any two IFVs have been proposed, some shortcomings, such as inadmissibility, nonrobustness, and nondeterminacy, may exist when these orders are utilized. Inspired by the Euclidean approach for ranking IFVs, we present a novel order that can overcome the aforementioned shortcomings using the notion of relative geometric distance. With the help of graphic representation of an IFV, we analyze the existing popular approaches for ranking IFVs and point out their drawbacks. Taking into account these three distances between an IFV and the ideal negative point, ideal positive point and most uncertain point, respectively, we present a relative-distance-based mensuration for describing the favorable degree of the IFV. Accordingly, the boundaries used in the existing ranking approaches for IFVs are replaced by a novel curve. We prove that the proposed method satisfies the admissibility, robustness, and determinacy requirements. Finally, we extend the presented ranking method for IFVs by introducing human attitudes and compare the proposed approach with the existing ones, which indicates its availability and rationality. We then can obtain the conclusion that the relative distance is an effective and reasonable approach for ranking IFVs.