  A deep convolutional fuzzy system (DCFS) on a high-dimensional input space is
a multi-layer connection of many low-dimensional fuzzy systems, where the input
variables to the low-dimensional fuzzy systems are selected through a moving
window across the input spaces of the layers. To design the DCFS based on
input-output data pairs, we propose a bottom-up layer-by-layer scheme.
Specifically, by viewing each of the first-layer fuzzy systems as a weak
estimator of the output based only on a very small portion of the input
variables, we design these fuzzy systems using the WM Method. After the
first-layer fuzzy systems are designed, we pass the data through the first
layer to form a new data set and design the second-layer fuzzy systems based on
this new data set in the same way as designing the first-layer fuzzy systems.
Repeating this process layer-by-layer we design the whole DCFS. We also propose
a DCFS with parameter sharing to save memory and computation. We apply the DCFS
models to predict a synthetic chaotic plus random time-series and the real Hang
Seng Index of the Hong Kong stock market.
