Effective personnel assignment is one of the most crucial tasks performed by the decision makers of a company. This paper proposes a systematic approach with a feedback mechanism in which the interdependences among positions and the differences among the selected employees are considered simultaneously. Unfortunately, the two combined considerations have rarely been discussed in the literature. The purpose of this approach is to obtain the best matching of candidates and positions in order to organize a collaboratively cross-functional team. In a fuzzy environment and, then, in the proposed approach, a bi-objective binary integer programming (BOBIP) model is formulated. Based on the weighted composite scores determined in the third step of the proposed procedure, the BOBIP model is transformed into a fuzzy bi-objective goal programming (FBOGP) model. An elaborately designed heuristic algorithm is developed to determine the appropriate values of several important parameters in the FBOGP model, which is solved using LINDO 8.0. An application example is illustrated, and two additional examples are tested. The results indicate that the proposed approach achieves the acceptable satisfaction level and requires less computation time than the brute force enumerative method.