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Image segmentation is an important component in image processing, pattern recognition and computer vision. Many segmentation algorithms have been proposed. However, segmentation methods for both noisy and noise-free images have not been studied in much detail. Neutrosophic set (NS), a part of neutrosophy theory, studies the origin, nature, and scope of neutralities, as well as their interaction with different ideational spectra. However, neutrosophic set needs to be specified and clarified from a technical point of view for a given application or field to demonstrate its usefulness. In this paper, we apply neutrosophic set and define some operations. Neutrosphic set is integrated with an improved fuzzy c-means method and employed for image segmentation. A new operation, α-mean operation, is proposed to reduce the set indeterminacy. An improved fuzzy c-means (IFCM) is proposed based on neutrosophic set. The computation of membership and the convergence criterion of clustering are redefined accordingly. We have conducted experiments on a variety of images. The experimental results demonstrate that the proposed approach can segment images accurately and effectively. Especially, it can segment the clean images and the images having different gray levels and complex objects, which is the most difficult task for image segmentation. [ABSTRACT FROM AUTHOR]