Backpropagation in neural networks with fuzzy conjunction units

An approach that generalizes the backpropagation learning rule such that it can be applied to multilayered neural networks involving fuzzy conjunction units is presented. The output of a fuzzy conjunction unit is computed by taking the minimum of all its inputs. The approach uses hill-climbing search at conjunction units where the backpropagation rule fails to apply because the transfer function is not differentiable. Error propagation at conjunction units requires analysis of error dependency across conjunction. When there are multiple alternatives for error adaptation at a conjunction unit, the choice is the one that allows the system to be modified the best. This approach is evaluated by simulation and compared with the approach which turns a conjunction unit into a pi unit. The results show that the hill-climbing approach is always equal to or better than the other approach in terms of the error at the end of training, but the speed of convergence may be slower in some cases