Most image processing and computer vision applications require edge detection for object recognition, image segmentation, and scene analysis. The traditional algorithms cannot handle the demanding requirements on the accuracy and robustness of these applications. Information set theory is utilized in this paper for defining edge strength measures which help in finding robust edges. The proposed work is originated from the smallest univalue segment assimilating nucleus concept, wherein a mask is applied on the red, green, and blue components of the color image for calculating a small area of neighboring pixels with similar brightness to center pixels. A symmetric Gaussian membership function (MF) is used to fuzzify the histogram of this area. This MF is converted into sigmoidal MF to strengthen and sharpen the weak edges. These two MFs provide the best results in comparison to other MFs used in literature. Extensive simulation results show that the proposed technique produces better results than other existing techniques in terms of the qualitative and quantitative measures, which include Pratt’s figure of merit, structural similarity index, and analysis of variance. The proposed technique also works well in the presence of impulse noise.