Multi-indicator matrices represent a set of objects or alternatives characterized simultaneously by several criteria or attributes. In many situations, a decision-maker is interested in assessing each object, by considering simultaneously all criteria, and defining a ranking able to synthesize the global characteristic of each object, for example, from best to worst. However the assessment could be influenced by uncertain factors. For example, the cost of a project could be affected by variations in the interest rate. The effects of such variations could affect the initial or base rank. In this paper, the robustness of the base rank is analyzed. The first part analyzes how the uncertainty in the numerical value of the criteria associated to each objects affects its rank. Additionally, it proposes some ideas for assessing the rank robustness. The second part proposes the use of global sensitivity analysis to assess the importance of each uncertain factor on, for example, the base rank. An example related to a real portfolio management, using three techniques that do not require additional preference parameters is presented.