A vital activity is the issue of creating a knowledge society, which can only be solved by involving all the forces of intellectual, academic, all generators of ideas. The paper is intended as a contribution, along with attempts by other specialists in finding operational solutions and their implementation in estimating the risk of bankruptcy and predicting its occurrence so through research and development, education and innovation can bring prosperity, development sustainable and personal development of every citizen. Scientific novelty and originality of research and of the results obtained is to formulate proposals of rates in the score function of economic models to estimate the risk of bankruptcy of firms. This rate takes into account intangible assets predominant factor in the evolution of the company and the market value of the company. On the basis of an analysis made it demonstrated that score function for models Altman, Conan-Holder and Rating suffered a pretty significant change if we took into account the intangible assets of the company. Entering this rate into the mentioned models was made using expert systems and neural networks. The analysis, arguments, mathematical models, principles, goals can all be made based on the methodology of scientific research in the creation of knowledge society, scientific elaborations. The results of the work can be applied to all firms in the EU countries' national economies. The mathematical model could have other economic interpretations and therefore can be used in formulating and solving a number of problems in the national economies.