Hesitant fuzzy C-means algorithm and its application in image segmentation

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.