The paper presents the FUCOM-FMAIRCA MCDM model for application in human resource management. The proposed model allows the inclusion of all relevant stakeholders in the process of human resource selection, enhances the pool of scientific knowledge in the field of human resource management highlighting selection as a special activity, and uses modern quantitative (mathematical) decision-making methods. Based on the analysis of personality traits of teachers and literature related to this field, the necessary characteristics of teachers of the Military Academy are presented, on the basis of which the selection criteria are formed. The FUCOM method was used to define the weight coefficients of the defined criteria. In order to more precisely determine the qualitative properties and their quantification, triangular fuzzy numbers were implemented in the MAIRCA method, and by applying all the steps of this method, the ranking of alternatives was performed. Finally, in order to test the validity of the model, a sensitivity analysis was carried out.