Efficient human resource management needs accurate assessment and representation of available competences as well as effective mapping of required competences for specific jobs and positions. In this regard, appropriate definition and identification of competence gaps express differences between acquired and required competences. Using a detailed quantification scheme together with a mathematical approach is a way to support accurate competence analytics, which can be applied in a wide variety of sectors and fields. This article describes the combined use of software technologies and mathematical and statistical methods for assessing and analyzing competences in human resource information systems. Based on a standard competence model, which is called a Professional, Innovative and Social competence tree, the proposed framework offers flexible tools to experts in real enterprise environments, either for evaluation of employees towards an optimal job assignment and vocational training or for recruitment processes. The system has been tested with real human resource data sets in the frame of the European project called ComProFITS.