The classical model of Fickian diffusion forms the basis for the study of the diffusive transport of chemical species in fluid-saturated porous media. In this paper, we examine the problems related to in-plane diffusive transport in a thin layer, the thickness of which is significantly smaller than the lateral dimensions, and where the diffusion coefficients are considered to be orthotropic. In particular, the emphasis of the paper is on the incorporation of fuzzy set theory in the description of the two principal diffusivity coefficients governing the contaminant transport in the porous medium. The results presented in the paper illustrate the influence of fuzzy descriptions of the orthotropic diffusivity characteristics of the medium on the time-dependent distribution of the concentration.