Fuzzy arithmetic is employed for the analysis of uncertainties in water-stream pollution, when the various model parameters involved are imprecise. The one-dimensional advection–dispersion equation, for both a conservative and a non-conservative substance, was solved analytically for point and Gaussian-hill input loads of pollution, considering the dispersion and decay coefficients involved as fuzzy numbers. The solution of the advection–dispersion equation was also conducted numerically for the same input loads with the finite-difference method, employing a Lagrangian–Eulerian scheme. The good agreement between analytical and numerical results presented in the form of fuzzy numbers confirms the reliability of the numerical scheme. The advection–dispersion equation of a non-conservative substance was then solved numerically for ten different water quality parameters, in order to study the water pollution in a water stream. The dispersion coefficient, the source terms and the input loads were expressed as fuzzy numbers, and the concentration of each quality parameter was obtained in fuzzy-number form. With fuzzy modeling, imprecise data can be represented and imprecise output produced, with minimal input data requirements and without the need of a large number of computations.