This paper presents a novel calculation of fuzzy exponent in the sigmoid functions for fuzzy neural networks. The investigated fuzzy neural network applies fuzzy input signals and crisp connection weights in the network's hidden and output layers. The applied calculation of fuzzy exponent is based on a parametric representation of the fuzzy exponent that is able to provide a crisp output instead of the extension principle's fuzzy output and requires significantly less computational effort than the learning based on α-cuts. For the training of the network the bacterial memetic algorithm is applied which effectively combines the bacterial evolutionary algorithm with gradient based learning. The method is tested on a benchmark problem and on two real datasets. Comparison to the classical technique concerning the learning time is also provided in the paper. © 2013 Elsevier B.V.