This paper delves into classification tasks, where data is categorized into binary classes, such as fraudulent/non-fraudulent or sick/not sick as example. Employing a statistical approach, this task entails utilizing hypothesis testing. Tuning this test involves selecting an acceptable risk alpha (associated with false positives), thereby implicating a beta risk (related to false negatives). In classification challenges, the principal aim is to mitigate the misclassification rate. However, the determination of these two risks is not be discretionary but rather enforced by the learning process, particularly evident when employing neural networks. This paper seeks to propose a modification of the learning algorithm for multilayer perceptron aimed at effectively balancing these risks. This adaptation hinges on leveraging a weighted criterion to minimize errors, accounting for the signs of different error types. This methodology is assessed across two benchmarks: a simulated dataset and a genuine medical dataset.