Atomic properties of $n=3$ levels for ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ ions ($Z=74$) are systematically calculated using two different and independent methods, namely, the second-order many-body perturbation theory and the multiconfiguration Dirac-Hartree-Fock method combined with the relativistic configuration interaction approach. Wavelengths and transition rates for electric- and magnetic-dipole transitions involving the $n=3$ levels of ${\mathrm{W}}^{47+}\ensuremath{-}{\mathrm{W}}^{55+}$ are calculated. In addition, we discuss in detail the importance of the valence and core-valence electron correlations, the Breit interaction, the higher-order frequency-dependent retardation correction, and the leading quantum electrodynamical corrections for transition wavelengths. Spectroscopic accuracy is achieved for the present calculated wavelengths, and most of them agree with experimental values within $0.05%$. Our calculated wavelengths, combined with collisional radiative model simulations, are used to identify the yet unidentified 25 observed lines in the extremely complex spectrum between $27\phantom{\rule{0.16em}{0ex}}\AA{}$ and $34\phantom{\rule{0.16em}{0ex}}\AA{}$ measured by Lennartsson $et\phantom{\rule{4pt}{0ex}}al.$ [Phys. Rev. A 87, 062505 (2013)]. We provide additional data for 472 strong electric-dipole transitions in the wavelength range of 17--50 \AA{}, and 185 strong magnetic-dipole transitions between $36\phantom{\rule{0.16em}{0ex}}\AA{}$ and $4384\phantom{\rule{0.16em}{0ex}}\AA{}$, with a line intensity greater than $1\phantom{\rule{0.16em}{0ex}}\mathrm{photon}/\mathrm{s}$. These can provide benchmark data for future experiments and theoretical calculations.