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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.Preprint. Under review.

Adaptive neuro-complex-fuzzy inference system (ANCFIS) is a neurofuzzy system that employs complex fuzzy sets for time-series forecasting. One of the particular advantages of this architecture is that each input to the network is a windowed segment of the time series, rather than a single lag as in most other neural networks. This allows ANCFIS to predict even chaotic time series very accurately, using a small number of rules. Some recent findings, however, indicate that published results on ANCFIS are suboptimal; they could be improved by changing how the length of an input window is determined, and/or subsampling the input window.We compare the performance of ANCFIS using three different approaches to defining an input window, across six time-series datasets. These include chaotic datasets and time series up to 20,000 observations in length. We found that the optimal choice of input formats was dataset dependent, and may be influenced by the size of the dataset. We finally develop a recommended approach to determining input windows that balances the twin concerns of accuracy and computation time. IntroductionTime-series forecasting has emerged as the first major application of complex fuzzy sets and logic, which were first described by Ramot in [1]. Beginning in 2007, complex-valued neuro-fuzzy systems were developed to inductively learn forecasting models; these include the adaptive neuro-complex-fuzzy inference system (ANCFIS) architecture [2], and the family of complex neuro-fuzzy system (CNFS) architectures [3]. Both ANCFIS and CNFS are modifications of the well-known ANFIS architecture, in which complex fuzzy sets and complex-valued network signals are used. These architectures showed that complex fuzzy sets were naturally useful in creating very accurate forecasting models. ANCFIS in particular is also very parsimonious;

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