Image segmentation plays an important role in many fields such as computer vision, pattern recognition, machine learning and so on. In recent years, many variants of standard fuzzy C-means (FCM) algorithm have been proposed to explore how to remove noise and reduce uncertainty. In fact, there are uncertainty on the boundary between different patches in images. Considering that hesitant fuzzy set is a useful tool to deal with uncertainty, in this paper, we merge hesitant fuzzy set with fuzzy C-means algorithm, introduce a new kind of method of fuzzification and defuzzification of image and the distance measure between hesitant fuzzy elements of pixels, present a method to establish hesitant membership degree of hesitant fuzzy element, and propose hesitant fuzzy C-means (HFCM) algorithm. Finally, we compare our proposed HFCM algorithm with some existing fuzzy C-means (FCM) algorithms, and apply HFCM algorithm in natural image, BSDS dataset image, different size images and multi-attribute decision making. These numerical examples illustrate the validity and applicability of our proposed algorithm including its comprehensive performance, reducing running time and almost without loss of accuracy.

中文翻译：

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犹豫模糊C均值算法及其在图像分割中的应用

图像分割在许多领域都扮演着重要的角色，例如计算机视觉，模式识别，机器学习等。近年来，已经提出了许多标准模糊C均值（FCM）算法的变体，以探索如何消除噪声和减少不确定性。实际上，图像中不同色块之间的边界存在不确定性。考虑到犹豫模糊集是处理不确定性的有用工具，本文将犹豫模糊集与模糊C-均值算法相结合，介绍了一种新型的图像模糊和去模糊方法以及犹豫模糊元素之间的距离测度提出了一种建立犹豫模糊元的犹豫隶属度的方法，并提出了犹豫模糊C均值算法。最后，我们将我们提出的HFCM算法与一些现有的模糊C均值（FCM）算法进行了比较，并将HFCM算法应用于自然图像，BSDS数据集图像，不同大小的图像和多属性决策。这些数值示例说明了我们提出的算法的有效性和适用性，包括其综合性能，减少了运行时间并且几乎没有损失准确性。