  This study is inspired by those of Huang et al. (Soft Comput. 25, 2513--2520,
2021) and Wang et al. (Inf. Sci. 179, 3026--3040, 2009) in which some ranking
techniques for interval-valued intuitionistic fuzzy numbers (IVIFNs) were
introduced. In this study, we prove that the space of all IVIFNs with the
relation in the method for comparing any two IVIFNs based on a score function
and three types of entropy functions is a complete chain and obtain that this
relation is an admissible order. Moreover, we demonstrate that IVIFNs are
complete chains to the relation in the comparison method for IVIFNs on the
basis of score, accuracy, membership uncertainty index, and hesitation
uncertainty index functions.
