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Convolutional operations extracting effective features have been widely used in the field of deep learning. For the convolution is difficult to process set data, we propose two convolutional operators on fuzzy sets, and build a fuzzy granular classifier. Firstly, a fuzzy granulation is performed on single-atom features of classification systems to form fuzzy conditional granules and fuzzy decision granules. Then, a fuzzy conditional granular vector is constructed from the fuzzy conditional granules, and a convolutional operation is carried out on the granular vector. After that, a new fuzzy feature granule is obtained. The fuzzy feature granule is compared with its corresponding fuzzy decision granule. The result of comparison is back-propagated to the fuzzy granular vector. Simultaneously, weights of the fuzzy granular vector are modified. Thus, a fuzzy granular convolutional classifier is formed by iterating and optimizing the weights of fuzzy granular vectors several times. Furthermore, we prove the difference and derivative of fuzzy granular convolution, which provide a theoretical basis for the back-propagation of the fuzzy granular convolutional classifier. Finally, the convergence effects of the fuzzy granular convolutional operations and the classification performance of the proposed classifier are tested on some UCI datasets. The theoretical analysis and experimental results show that the convolutional operations of fuzzy granular vectors have the characteristics of fast convergence, and the fuzzy granular convolutional classifier obtains a better classification performance. [ABSTRACT FROM AUTHOR]

Rough Cognitive Networks (RCNs) are a kind of granular neural network that augments the reasoning rule present in Fuzzy Cognitive Maps with crisp information granules coming from Rough Set Theory. While RCNs have shown promise in solving different classification problems, this model is still very sensitive to the similarity threshold upon which the rough information granules are built. In this paper, we cast the RCN model within the framework of fuzzy rough sets in an attempt to eliminate the need for a user-specified similarity threshold while retaining the model’s discriminatory power. As far as we know, this is the first study that brings fuzzy sets into the domain of rough cognitive mapping. Numerical results in the presence of 140 well-known pattern classification problems reveal that our approach, referred to as Fuzzy-Rough Cognitive Networks , is capable of outperforming most traditional classifiers used for benchmarking purposes. Furthermore, we explore the impact of using different heterogeneous distance functions and fuzzy operators over the performance of our granular neural network. [ABSTRACT FROM AUTHOR]