Dispensability of Bias for Three-layer Max-min Fuzzy Neural Networks

It is well-known that a conventional feedforward neural network always has bias (threshold) 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. We consider a three layers max-min FNNs, and prove that the bias indeed can be useless in certain cases specified in this paper.