Breast Cancer is one of the common and dangerous among women at the age of forty, so it is better for woman to have mammography testing as a significant step for the early detection of breast cancer and is diagnosis for treatment; There is an important need to an algorithm is used to determine the boundaries of the tumor in a finite accuracy. In this work, two algorithms were built depending on clustering approach as segmentation method. In the first algorithm has employed (K-mean) method, whilst in the second algorithm has employed fuzzy c-mean method (FCM). In both, the lazy snapping algorithm was used as an additional step to improve the segmentation performance of the detection of abnormal area. The proposed methods have been tested using mini-MIAS database, after assessment the results obtained. it indicates the accuracy of segmentation first algorithm, are 91.18% and accuracy of second algorithm is 94.12%. from results, it concludes that the proposed second algorithm is capable of estimate breast abnormal region boundary at high accuracy because it used fuzzy logic technique.