Set-valued algorithms are designed in this work to compute rigorous bounds of the unknown inputs of uncertain discrete-time linear systems. First, based on the classical full-order and reduced-order unknown input observers, non-conservative numerical schemes are proposed to characterize the reachable set of the estimation error. Then, by using these results, set-membership estimators of the unknown inputs are presented. Moreover, the results of these estimators can be merged together via set-intersection operators to obtain more accurate estimates.