The current study introduces a novel approach to estimate the incipient motion of sediments under a wide range of flow regimes by developing a fuzzy model with a fuzzy-band that refers to a transition from weak motion to general motion of sediment. The partial sediment entrainment is defined by fuzzy sets considering the uncertainty related to the individual ratio of inertia to viscous forces which is the definition of shear Reynolds number. In the current study, the Mamdani Fuzzy Inference System (Mamdani FIS) is used to develop a comprehensive fuzzy model of the incipient motion of sediment. The Mamdani FIS has a shortcoming regarding the training of the fuzzy model. To estimate the dimensionless shear stress, a new method is developed by combining a genetic algorithm with the fuzzy approach which is named the Geno-Mamdani Fuzzy Inference System (GMFIS) method. The performance of the GMFIS model is evaluated using experimental data by considering root mean square error (RMSE), Nash-Sutcliffe coefficient of efficiency (CE), degree of robustness (D-r), and concordance coefficient (CC) as evaluation criteria. The GMFIS model performed very well based on the RMSE, CE, D-r, and CC values and satisfactorily represented the three types of incipient motion. Finally, a new range of fuzzy, dimensionless, critical shear stress values is established in all flow conditions from weak to general sediment entrainment. (C) 2020 International Research and Training Centre on Erosion and Sedimentation/the World Association for Sedimentation and Erosion Research. Published by Elsevier B.V. All rights reserved.