This paper describes an approach for singularity (cores and deltas) detection on fingerprint images which uses fuzzy concepts and hierarchical structure. Singularity detection is usually performed of a discrete orientation matrix. Each of the elements of this matrix represents the dominant orientation on a given region. In this case, a fuzzy description of the orientation is defined. A very common method for singularity detection is the evaluation of the Poincare index on the orientation matrix. The fuzzy orientation is then naturally extended to the Poincare index. A multi-resolution description of the orientation matrix is developed and applied in a hierarchical way to estimate the location of singularities in fingerprint images. The method is illustrated on a database consisting of 310 fingerprints with mixed quality with application to fingerprint verification. The performance of this procedure is better than 98%.