The individual monitoring of internal exposure of workers comprises two steps: measurement and measurement interpretation. The latter consists in reconstructing the intake of a radionuclide from the activity measurement and calculating the dose using a biokinetic model of the radionuclide behavior in the human body. Mathematically, reconstructing the intake is solving an inverse problem described by a measurement-model equation. The aim of this paper is to propose a solution to this inverse problem when the measurement-model parameters are considered as uncertain. For that, an analysis of the uncertainty on the intake calculation is performed taking into account the dispersion of the measured quantity and the uncertainties of the measurement-model parameters. It is shown that both frequentist and Bayesian approaches can be used to solve the problem according to the measurement-model formulation. A common calculation algorithm is proposed to support both approaches and applied to the examples of tritiated water intake and plutonium inhalation by a worker.