Subjective evaluation is a commonly used method in the real recognition process. Generally, two fuzziness can be found in evaluation information, namely what values should be given to fully describe the information and how to distinguish different values. The recently developed probabilistic hesitant fuzzy set could perfectly address these issues. In this article, we propose a dual-fuzzy convolutional neural network (DF-CNN) by fusing the hot neural network algorithm into the probabilistic hesitant fuzzy environment and then using it in a practical handwritten image recognition process. For this new DF-CNN, we provide the whole calculation process including the forward propagation, backward propagation, and parameter updating calculations. Also, the optimization algorithm of the DF-CNN is given to derive its optimal results. Finally, we apply the DF-CNN and its optimization algorithm to deal with a real issue, namely the handwritten numeral image recognition. The calculation process and the comparison fully demonstrate the feasibility and effectiveness of the proposed new model and algorithm.

中文翻译：

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处理手写图像识别的双模糊卷积神经网络

主观评价是现实识别过程中常用的方法。通常，评价信息中存在两个模糊性，即应该赋予什么值才能充分描述信息，以及如何区分不同的值。最近开发的概率犹豫模糊集可以完美地解决这些问题。在本文中，我们通过将热神经网络算法融合到概率犹豫模糊环境中，然后将其用于实际的手写图像识别过程，提出了一种双模糊卷积神经网络 (DF-CNN)。对于这个新的 DF-CNN，我们提供了包括前向传播、反向传播和参数更新计算在内的整个计算过程。此外，还给出了 DF-CNN 的优化算法，以得出其最优结果。最后，我们应用 DF-CNN 及其优化算法来处理一个实际问题，即手写数字图像识别。计算过程和对比充分证明了所提新模型和算法的可行性和有效性。