Sediment incipient motion in turbulent flow conditions is hard to be determined due to the random turbulence fluctuations as well as the random positioning and orientation of the sediment particles. The most common criteria for the initiation of motion of sediment particles, like the Shields diagram, have a general movement or no-movement functionality. In such criteria, the subjectivity of the researcher on the definition of sediment incipient motion influences the quantification of sediment transport; however, uncertainties in the selection of critical flow conditions may lead to large computational errors. In order to avoid the ambiguity of selecting a unique entrainment threshold, this paper employed fuzzy regression and set a fuzzy band, which offers a transition from sporadic to general sediment entrainment. Two approaches were used, namely the conventional fuzzy regression analysis and a goal programming-based fuzzy regression. In the latter, the modification of the fuzzy linear regression basis, by establishing a distance (error) associated with the underestimation of the left-hand boundary and a distance associated with the overestimation of the right-hand boundary, constitutes a significant improvement in the field since it avoids the significant influence of the outliers. The fuzzy regression analyses employ data from the pertinent literature and consider critical shear stress to depend on a particle Reynolds number and relative roughness. The results show that the terms that contain the particle Reynolds number do not have any uncertainty, while the fuzziness appears in both the coefficient of the relative roughness and the constant terms.