Personnel evaluation and selection is an essential part of modern business. Appropriate candidate selection can significantly contribute to companies in terms of increased profit, good culture, reputation, reduced costs, etc. This paper addresses the personnel evaluation and selection problem at the University of Pardubice, Faculty of Transport Engineering (UPCE). Since this is a typical ranking alternative problem where multiple criteria affect the decision, the Z-numbers-based Alternative Ranking Order Method Accounting for the two-step Normalization (AROMAN) is applied. Four Ph.D. candidates are assessed, and the most appropriate is selected to be employed by the UPCE. The Z-numbers fuzzy AROMAN method ranks Ph.D. candidate number four as the most appropriate alternative. To investigate the stability and sensitivity of the Z-numbers fuzzy AROMAN method, the values of parameters β and λ used in the mathematical calculations of the method were changed. The results of sensitivity analysis revealed that the obtained solution is stable. To confirm the robustness of the proposed approach, a comparative analysis is performed. Simple Additive Weighting (SAW), Weighted Product Model (WPM), and Z-number fuzzy TOPSIS were applied. Besides, we applied the fuzzy inferior ratio method as well. The results confirm the high robustness of the proposed Z-numbers fuzzy AROMAN method.