To stimulate the development of the Internet of Health Things and the construction of a robotic automation system in the healthcare industry, the mobile robot selection problem for a hospital pharmacy is studied. We target the mobile robot selection as a multi-criteria decision-making problem. The VIKOR-based implementation steps integrating fuzzy extended analytic hierarchy process technique are developed. To avoid any loss of information and ensure the veracity of the VIKOR-based calculations, we employ the fuzzy ranking technique based on the degree of possibility to select the best mobile robot alternative by deriving the minimum fuzzy comprehensive utility value. The results of a case study and the accompanying sensitivity analysis show the effectiveness and robustness of the fuzzy extended VIKOR approach for the mobile robot selection problem.