We are interested in finding and characterizing the symmetry planes of fuzzy objects in 3D space. We introduce first a fuzzy symmetry measure which defines an object symmetry degree with respect to a given plane. It is computed by measuring the similarity between the original object and its reflection. The choice of an appropriate measure of comparison is based on the desired properties. In a second part, a method for finding the best symmetry planes of fuzzy objects is proposed. We then apply these results to the representation of directional relationships .