Consistency of 2D and 3D distances of intuitionistic fuzzy sets

► Consistency criteria are defined to compare different distances between IFSs. ► 2D distances and their 3D counterparts are shown to be inconsistent. ► When applied to a set of IFSs may provide a different ordering or representation. ► A new 3D Extended Hausdorff distance between IFSs is proposed and studied.