  The effect of coupling between pairing and quadrupole triaxial shape
vibrations on the low-energy collective states of $\gamma$-soft nuclei is
investigated using a model based on the framework of nuclear energy density
functionals (EDFs). Employing a constrained self-consistent mean-field (SCMF)
method that uses universal EDFs and pairing interactions, potential energy
surfaces of characteristic $\gamma$-soft Os and Pt nuclei with $A\approx190$
are calculated as functions of the pairing and triaxial quadrupole
deformations. Collective spectroscopic properties are computed using a
number-nonconserving interacting boson model (IBM) Hamiltonian, with parameters
determined by mapping the SCMF energy surface onto the expectation value of the
Hamiltonian in the boson condensate state. It is shown that, by simultaneously
considering both the shape and pairing collective degrees of freedom, the
EDF-based IBM successfully reproduces data on collective structures based on
low-energy $0^{+}$ states, as well as $\gamma$-vibrational bands.
