System size dependence of particle-ratio fluctuations in Pb+Pb collisions at 158$A$ GeV

New measurements by the NA49 experiment of the centrality dependence of event-by-event fluctuations of the particle yield ratios (K$^{+}$+K$^{-}$)/($pi^{+}+pi^{-}$), (p+$bar{text p}$)/($pi^{+}+pi^{-}$), and (K$^{+}$+K$^{-}$)/(p+$bar{text p}$) are presented for Pb+Pb collisions at 158$A$ GeV. The absolute values of the dynamical fluctuations of these ratios, quantified by the measure $sigma_{text{dyn}}$, increase by about a factor of two from central to semi-peripheral collisions. Multiplicity scaling scenarios are tested and found to apply for both the centrality and the previously published energy dependence of the (K$^{+}$+K$^{-}$)/($pi^{+}+pi^{-}$) and (p+$bar{text p}$)/($pi^{+}+pi^{-}$) ratio fluctuations. A description of the centrality and energy dependence of (K$^{+}$+K$^{-}$)/(p+$bar{text p}$) ratio fluctuations by a common scaling prescription is not possible since there is a sign change in the energy dependence.