Description: This article describes the main approaches and models for assessment of professional level of competence, and suggests criteria for evaluating the effectiveness of competencies. We propose a mathematical model for the staff selection based on the analysis of competencies prototypes. To substantiate consistent decision-making in the management of personnel proposed to use the concept of Pareto dominance. The problem under consideration belongs to the class of multiobjective optimization. To overcome the complexity of calculating the function criteria the fuzzy inference algorithm is used.
Keywords: regression analysis, the model value-added measure (VMA), effective functioning, the educational process, high schools