Liver tumor segmentation from computed tomography (CT) images is a critical and challenging task. Due to the fuzziness in the liver pixel range, the neighboring organs of the liver with the same intensity, high noise and large variance of tumors. The segmentation process is necessary for the detection, identification, and measurement of objects in CT images. We perform an extensive review of the CT liver segmentation literature. Furthermore, in this paper, an improved segmentation approach based on watershed algorithm, neutrosophic sets (NS), and fast fuzzy c-mean clustering algorithm (FFCM) for CT liver tumor segmentation is proposed. To increase the contrast of the liver CT images, the intensity values are adjusted and high frequencies are removed using histogram equalization and median filter approach. It is followed by transforming the CT image to NS domain, which is described using three subsets (percentage of truth T, the percentage of indeterminacy I, and percentage of falsity F). The obtained NS image is enhanced by adaptive threshold and morphological operators to focus on liver parenchyma. The enhanced NS image passed to a watershed algorithm for post-segmentation process and liver parenchyma is extracted using the connected component algorithm. Finally, the liver tumors are segmented from the segmented liver using fast fuzzy c-mean (FFCM). A quantitative analysis is carried out to evaluate segmentation results using six different indices. The results show that the overall accuracy offered by the employed neutrosophic sets is accurate, less time consuming, less sensitive to noise and performs better on non-uniform CT images.