This paper proposes a new model based on Fuzzy k-Nearest Neighbors for classification with monotonic constraints, Monotonic Fuzzy k-NN (MonFkNN). Real-life data-sets often do not comply with monotonic constraints due to class noise. MonFkNN incorporates a new calculation of fuzzy memberships, which increases robustness against monotonic noise without the need for relabeling. Our proposal has been designed to be adaptable to the different needs of the problem being tackled. In several experimental studies, we show significant improvements in accuracy while matching the best degree of monotonicity obtained by comparable methods. We also show that MonFkNN empirically achieves improved performance compared with Monotonic k-NN in the presence of large amounts of class noise.