  We derive an entropic uncertainty relation for generalized
positive-operator-valued measure (POVM) measurements via a direct-sum
majorization relation using Schur concavity of entropic quantities in a
finite-dimensional Hilbert space. Our approach provides a significant
improvement of the uncertainty bound compared with previous majorization-based
approaches [S. Friendland, V. Gheorghiu and G. Gour, Phys. Rev. Lett. 111,
230401 (2013); A. E. Rastegin and K. \.Zyczkowski, J. Phys. A, 49, 355301
(2016)], particularly by extending the direct-sum majorization relation first
introduced in [\L. Rudnicki, Z. Pucha{\l}a and K. \.{Z}yczkowski, Phys. Rev. A
89, 052115 (2014)]. We illustrate the usefulness of our uncertainty relations
by considering a pair of qubit observables in a two-dimensional system and
randomly chosen unsharp observables in a three-dimensional system. We also
demonstrate that our bound tends to be stronger than the generalized
Maassen--Uffink bound with an increase in the unsharpness effect. Furthermore,
we extend our approach to the case of multiple POVM measurements, thus making
it possible to establish entropic uncertainty relations involving more than two
observables.
