This contribution explores the way of accomplishing a TOPSIS ranking of various submitted variants taking into account (a) our newly-developed notions of variant superiority, inferiority and noninferiority multiattribute canonical fuzzy bags defined on attributes and (b) making use of bag metrics to compute the relative closeness of the different variants to an ideal solution. In particular, we prove the existence and the uniqueness of a bag metric fulfilling a number of interesting properties.