A study of suitable analytic formulations for each of /spl Fscr/, /spl Gscr/, and /spl Hscr/ components of the hierarchical model is conducted. The primary examples of the companion paper (Barsala et al., 1999) are established as representative of the necessary general properties. Further extensions to fuzzy sets as arguments of /spl Fscr/-comparison and /spl Gscr/- and /spl Hscr/- aggregation are discussed.