This paper is a continuation of our previous works on geometric similarity measures between Atanassov’s intuitionistic fuzzy sets (A-IFSs for short). We consider some traps of the straightforward approach in the case of A-ISs while similarity is understood as a dual concept of a distance. The difficulties are a result of, first, the symmetry of the three terms (the membership, nonmembership and hesitation margin) in an A-IFS element description, and second, of an important role played by those three terms in the definition of the complement of the A-IFS which should be taken into account in the similarity measures.