  The use, for flavor symmetries, of the quantum (or q-) analogs of unitary
groups SU(n_f) yields new, very accurate, baryon mass sum rules. We show, in
the 3-flavor case, that such approach accounts for nonpolynomial SU(3)-breaking
effects in the octet and decuplet baryon masses. A version of this approach
with manifestly q-covariant mass operator is given. The obtained new version of
the q-deformed mass relation is simpler than those derived before, but, for its
empirical validity, the parameter q is to be fixed by fitting. As shown, the
well-known Gell-Mann--Okubo octet mass sum rule results, besides usual SU(3),
also from an exotic "symmetry" encoded in the singular case q=-1 of the
q-algebra U_q(su_3).
