<p>This manuscript describes a novel method for modelling pollutant transport in river system by combining fuzzy mathematics with the finite difference method (FDM). The proposed methodology utilises fuzzy partial differential equation (FPDE) to deal with uncertainties and ambiguous data in the modelling procedure. Incorporating fuzzy sets and fuzzy rules, the model depicts the complexity of pollutant transport and provides a more precise representation. Utilising the FDM to discretize the governing advection–diffusion equations enables efficient numerical simulation. Extensive numerical experiments demonstrate the efficacy of the fuzzy mathematics method in capturing pollutant behaviour and the superiority of the combined method. This research contributes to the advancement of pollutant transport modelling in river system and provides environmental scientists and engineers with valuable insights. </p>