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.

提取有效特征的卷积运算在深度学习领域得到了广泛的应用。针对卷积难以处理集合数据，我们在模糊集合上提出了两个卷积算子，并构建了一个模糊粒度分类器。首先对分类系统的单原子特征进行模糊粒化，形成模糊条件粒和模糊决策粒。然后，由模糊条件粒构造模糊条件粒向量，并对粒向量进行卷积运算。之后，得到一个新的模糊特征颗粒。将模糊特征粒与其对应的模糊决策粒进行比较。比较的结果被反向传播到模糊粒度向量。同时，修改模糊颗粒向量的权重。因此，通过多次迭代优化模糊粒向量的权重，形成模糊粒卷积分类器。进一步证明了模糊粒卷积的差分和导数，为模糊粒卷积分类器的反向传播提供了理论依据。最后，在一些 UCI 数据集上测试了模糊粒度卷积运算的收敛效果和所提出的分类器的分类性能。理论分析和实验结果表明，模糊粒向量的卷积运算具有收敛速度快的特点，模糊粒卷积分类器获得了较好的分类性能。