In a decision-based neural network(DBNN), the teacher only tells the correctness of the classification for each training pattern. In dealing with practical classification applications where significant overlap may exist between categories, a special care is needed to cope with the 'marginal' training patterns. For these situations, a soft decision is more appropriate. This motivates a fuzzy-decision neural network(FDNN) which incorporates a penalty criterion into the DBNNs. Following , a penalty function is proposed which treats the errors with equal penalty once the magnitude of error exceeds certain threshold. Theoretically, the FDNNs are less biased and they yield the minimum error rate when the number of the training patterns is very large. Simulation results confirm that the FDNN works more effectively than the DBNN when the training patterns are not separable.