The relative fibroglandular tissue content in the breast, commonly referred to as breast density, has been shown to be the most significant risk factor for breast cancer after age. Currently, the most common approaches to quantify density are based on either semi-automated methods or visual assessment, both of which are highly subjective. This work presents a novel multi-class fuzzy c-means (FCM) algorithm for fully-automated identification and quantification of breast density, optimized for the imaging characteristics of digital mammography. The proposed algorithm involves adaptive FCM clustering based on an optimal number of clusters derived by the tissue properties of the specific mammogram, followed by generation of a final segmentation through cluster agglomeration using linear discriminant analysis. When evaluated on 80 bilateral screening digital mammograms, a strong correlation was observed between algorithm-estimated PD% and radiological ground-truth of r=0.83 (p<0.001) and an average Jaccard spatial similarity coefficient of 0.62. These results show promise for the clinical application of the algorithm in quantifying breast density in a repeatable manner.