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.
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