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Skin lesion border irregularity, which represents the B feature in the ABCD rule, is considered one of the most significant factors in melanoma diagnosis. Since signs that clinicians rely on in melanoma diagnosis involve subjective judgment including visual signs such as border irregularity, this deems it necessary to develop an objective approach to finding border irregularity. Increased research in neural networks has been carried out in recent years mainly driven by the advances of deep learning. Artificial neural networks (ANNs) or multilayer perceptrons have been shown to perform well in supervised learning tasks. However, such networks usually don't incorporate information pertaining the ambiguity of the inputs when training the network, which in turn could affect how the weights are being updated in the learning process and eventually degrading the performance of the network when applied on test data. In this paper, we propose a fuzzy multilayer perceptron (F-MLP) that takes the ambiguity of the inputs into consideration and subsequently reduces the effects of ambiguous inputs on the learning process. A new optimization function, the fuzzy gradient descent, has been proposed to reflect those changes. Moreover, a type-II fuzzy sigmoid activation function has also been proposed which enables finding the range of performance the fuzzy neural network is able to attain. The fuzzy neural network was used to predict the skin lesion border irregularity, where the lesion was firstly segmented from the skin, the lesion border extracted, border irregularity measured using a proposed measure vector, and using the extracted border irregularity measures to train the neural network. The proposed approach outperformed most of the state-of-the-art classification methods in general and its standard neural network counterpart in particular. However, the proposed fuzzy neural network was more time-consuming when training the network.