A mathematical model is proposed that makes it possible to describe in a conceptual and functional aspect the formation and application of a knowledge base (KB) for an intelligent information system (IIS). This IIS is developed to assess the financial condition (FC) of the company. Moreover, for circumstances related to the identification of individual weakly structured factors (signs). The proposed model makes it possible to increase the understanding of the analyzed economic processes related to the company's financial system. An iterative algorithm for IIS has been developed that implements a model of cognitive modeling. The scientific novelty of the proposed approach lies in the fact that, unlike existing solutions, it is possible to adjust the structure of the algorithm depending on the characteristics of a particular company, as well as form the information basis for the process of assessing the company's FC and the parameters of the cognitive model.