Segmentation is an important step for the diagnosis of multiple sclerosis (MS). This paper presents a new approach to the fully automatic segmentation of MS lesions in Fluid Attenuated Inversion Recovery (FLAIR) Magnetic Resonance (MR) images. With the aim of increasing the contrast of the FLAIR MR images with respect to the MS lesions, the proposed method first estimates the fuzzy memberships of brain tissues (i.e., the cerebrospinal fluid (CSF), the normal-appearing brain tissue (NABT), and the lesion). The procedure for determining the fuzzy regions of their member functions is performed by maximizing fuzzy entropy through Genetic Algorithm. Research shows that the intersection points of the obtained membership functions are not accurate enough to segment brain tissues. Then, by extracting the structural similarity (SSIM) indices between the FLAIR MR image and its lesions membership image, a new contrast-enhanced image is created in which MS lesions have high contrast against other tissues. Finally, the new contrast-enhanced image is used to segment MS lesions. To evaluate the result of the proposed method, similarity criteria from all slices from 20 MS patients are calculated and compared with other methods, which include manual segmentation. The volume of segmented lesions is also computed and compared with Gold standard using the Intraclass Correlation Coefficient (ICC) and paired samples t test. Similarity index for the patients with small lesion load, moderate lesion load and large lesion load was 0.7261, 0.7745 and 0.8231, respectively. The average overall similarity index for all patients is 0.7649. The t test result indicates that there is no statistically significant difference between the automatic and manual segmentation. The validated results show that this approach is very promising.