  The combination of neural network and fuzzy systems into neuro-fuzzy systems
integrates fuzzy reasoning rules into the connectionist networks. However, the
existing neuro-fuzzy systems are developed under shallow structures having
lower generalization capacity. We propose the first end-to-end deep neuro-fuzzy
network and investigate its application for image classification. Two new
operations are developed based on definitions of Takagi-Sugeno-Kang (TSK) fuzzy
model namely fuzzy inference operation and fuzzy pooling operations; stacks of
these operations comprise the layers in this network. We evaluate the network
on MNIST, CIFAR-10 and CIFAR-100 datasets, finding that the network has a
reasonable accuracy in these benchmarks.
