New cross sections of the 183W(n,α)180mHf, 186W(n,d*)185Ta, 182W(n,p)182Ta, 184W(n,p)184Ta, 182W(n,2n)181W, 184W(n,α)181Hf and 186W(n,α)183Hf reactions were measured in the neutron energy range of 13.5-14.8 MeV via the activation technique with the aim to improve data base and resolve discrepancies. Monoenergetic neutrons in this energy range were produced via the T(d,n)4He reaction on a solid Ti-T target. The activities of the irradiated monitor foils and samples were measured by a well-calibrated high-resolution HPGe detector. Theoretical calculations of excitation functions of the seven nuclear reactions mentioned above in the neutron energies from the threshold to 20 MeV were performed using the nuclear theoretical model program system TALYS-1.9 with the aim to be expected to help with new evaluations of cross sections on tungsten isotopes. The experimental data obtained were analyzed and compared with previous experiments conducted by other researchers, the evaluated data available in the five major evaluated nuclear data libraries of IAEA (namely ENDF/B-VIII.0 or ENDF/B-VII.0, JEFF-3.3, JENDL-4.0u+, CENDL-3.2, BROND-3.1 or ROSFOND-2010), and the theoretical values acquired through TALYS-1.9 nuclear-reaction modeling tools. New cross section measurements agree with those of some recent experiments and theoretical excitation curves at the corresponding energies. The consistency of the theoretical excitation curves based on TALYS-1.9 with these experimental data is better than the evaluated curves available in the five major evaluated nuclear data libraries of IAEA.