This study presents a new robust method of developing quantitative structure-activity relationship (QSAR) models based on fuzzy mappings. An important issue in QSAR modelling is of robustness, i.e., model should not undergo overtraining and model performance should be least sensitive to the modelling errors associated with the chosen descriptors and structure of the model. We establish robust input-output mappings for QSAR studies based on fuzzy "if-then" rules. The identification of these mappings (i.e. the construction of fuzzy rules) is based on a robust criterion that the maximum possible value of energy-gain from modelling errors to the identification errors is minimum. The robustness of proposed approach has been illustrated with simulation studies and QSAR modelling examples. The method of robust fuzzy mappings has been compared with Bayesian regularized neural networks through the QSAR modelling examples of (1) carboquinones' data set, (2) benzodiazepine data set, and (3) predicting the rate constant for hydroxyl radical tropospheric degradation of 460 heterogeneous organic compounds.