Mathematical morphology (MM) is a powerful tool for spatial image processing. It was initially developed for single-band images, where each pixel has a scalar value, and it is easy to compare pixels in the neighbourhood of structuring elements (SEs) to identify local extrema for MM computation. However, applying MM to multiband images, where pixel values have vector representations, is not straightforward because there is no natural ordering between the vectors. In previous studies, several approaches have been proposed to extend MM to multiband images, but the definition of multivalued MM is not well agreed across these studies. This paper proposes using multicriteria decision-making systems to develop new vector ordering algorithms for multivalued MM computing. The effectiveness of the proposed algorithms is evaluated in multiband remote-sensing images by computing morphological descriptors on complex urban area data and comparing their results with those of conventional vector ordering methods. The obtained results demonstrate that the proposed multivalued MM tools achieve higher classification accuracies.