Most useful information in different kind of signals is usually carried by such singularities as the edges and peaks. Examples of such signals include Radar signals, the signals generated by the digital communication systems and biological signals (such as ECG, EEG and even medical images). Therefore, extraction and locating these singularities is a main and an initial common step in most of the signal and image processing application. In this paper a new multi-resolution based method for automatically extraction of singular points within the signals is presented where the information at various signal resolutions is combined together in a novel fuzzy manner. In the proposed algorithm, first, the multiresolution description of the signal is obtained using the wavelet transform. The information at each wavelet transform scale is next transformed into a fuzzy subset of the signal by means of appropriate fuzzy flying functions for each kind of the singularities (edges or peaks). The resulting fuzzy subsets describe to what degree any sample point from the signal domain can represent a Singularity at that particular scale. Finally, combining the information at various fuzzy subsets of the signal by means of the fuzzy operators, the sample points with the highest possibility of coincidence with a Singularity are identified. The superiority of the proposed algorithm in comparison to the commonly used techniques is shown using various synthetic and real signals.