||Similarity measures between images that are robust to noise and other kinds of distortion, while sensitive to transformations in a smooth and stable way, are of great importance in many image analysis problems. In this thesis project a family of measures based on fuzzy set theory, which combine shape and intensity, is extended to vector-valued fuzzy sets representing hybrid object representations such as intensity and gradient magnitude and multi-spectral images such as color images. Several novel distance measures are proposed, discussed with regards to theoretical and practical properties and evaluated empirically on both synthetic images and real-life object recognition and classification tasks. Performance metrics such as number of local minima and size of catchment basin which are important for distance-based local search techniques are evaluated for varying degrees of distortion by additive noise and number of discrete membership levels. The proposed distance measures are shown to enable utilization of information-rich object representations to outperform distance measures between scalar-valued fuzzy sets on various object detection and classification tasks.