  In this paper, first we present a new explanation for the relation between
logical circuits and artificial neural networks, logical circuits and fuzzy
logic, and artificial neural networks and fuzzy inference systems. Then, based
on these results, we propose a new neuro-fuzzy computing system which can
effectively be implemented on the memristor-crossbar structure. One important
feature of the proposed system is that its hardware can directly be trained
using the Hebbian learning rule and without the need to any optimization. The
system also has a very good capability to deal with huge number of input-out
training data without facing problems like overtraining.
