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 (a convolution operator) 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 can design these fuzzy systems using the WM Method. After the first-layer fuzzy systems are designed, we pass the data through the first layer and replace the inputs in the original data set by the corresponding outputs of the first layer to form a new data set , then we 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  we design the whole DCFS. Since the WM Method requires only one-pass of the data, this training algorithm for the DCFS is very fast . We apply the DCFS model with the training algorithm to predict a synthetic chaotic plus random time-series and the real Hang Seng Index of the Hong Kong stock market.
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.
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(a convolution operator)
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can
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and replace the inputs in the original data set by the corresponding outputs of the first layer
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, then we
and
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layer-by-layer
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Since the WM Method requires only one-pass of the data, this training algorithm for the DCFS is very fast
We also propose a DCFS with parameter sharing to save memory and computation
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model with the training algorithm
models