Neurocomputations in Relational Systems
IEEE Transactions on Pattern Analysis and Machine Intelligence
Identification of fuzzy relational equations by fuzzy neural networks
Fuzzy Sets and Systems
Improved fuzzy neural networks for solving relational equations
Fuzzy Sets and Systems
Classification of relational patterns as a decomposition problem
Pattern Recognition Letters
A dynamic neuro-fuzzy system configuration, stability, and fuzzy operational function
Fuzzy Sets and Systems
Quick fuzzy backpropagation algorithm
Neural Networks
Fuzzy relational neural network
International Journal of Approximate Reasoning
A new training algorithm for a fuzzy perceptron and its convergence
ISNN'05 Proceedings of the Second international conference on Advances in Neural Networks - Volume Part I
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It is well known that a conventional feedforward neural network always has bias terms, which is necessary for it to solve classification or approximation problems. But for fuzzy neural networks (FNNs), it seems not quite clear yet whether the bias is dispensable or not. Some authors introduce the bias, while the others do not. This note tries to partly answer this question for two simple building blocks of FNNs: fuzzy perceptron and max-min FNN. It is shown that the bias is basically dispensable for fuzzy perceptrons (max-min FNNs plus a sign function), which are usually used for classification. On the other hand, the bias is dispensable for max-min FNNs, which are used for both approximation and classification, if and only if a special condition is valid. But this special condition is generally not valid, or not easy to justify in practice. So the bias is generally indispensable for max-min FNNs.