The objective of this paper is to propose a filtering strategy for max-plus linear systems with bounded disturbances without the direct calculation of the a posteriori state probability. The strategy is based on the inversion of the expectation of the measure with respect to the state variable. Among the possible solutions, the closest to the prediction is chosen. An algorithm, based on interval propagation, is proposed to solve this problem. Simulations are performed to show the consistence of the proposed methodology with other approaches in the literature.