The article gives the rationale for the necessity of developing a theoretical and methodological basis of mass media theory and up-dating its research tools. It is shown that the main direction of further research should be its mathematization and software-based algorithm development of models for managing information flows. It is established that in order to implement this idea it is necessary to apply a process approach to mass media system research as solutions based on the process approach significantly increase the potential for planning and forecasting changes in the media system, as well as forming effective models of information flows management. In the framework of the process approach, mass information activities are considered as processes that result in creating an information product meeting the needs of a particular consumer or a group of consumers. By integrating all the information product processes that take place in media organizations, a process-type media system that in general results in meeting information needs of the society relevant to peoples interests, preferences and requests is formed. In order to study the system, the authors highlight its most important properties such as integrity, nonadditivity and focus. It is demonstrated that it is impossible to apply conventional mathematical methods and models in the conditions of transient influence of external factors and nonlinear interrelations between processes. The authors prove that revealed interrelations can be successfully visualized by means of cognitive mapping. The authors suggest а cognitive map for evaluation of mass media performance, where a target concept is the level of awareness of the population that provides them with landmarks to guide themselves in the world while governing concepts are the quantity demanded and supplied and the quality of information products. At the same time, it is specified that the quality of mass media products is determined by mass media accessibility, promptness, reliability and feedback from consumers. The proposed cognitive map is formalized by means of fuzzy information about concepts and power of their influence, which is presented in the form of a knowledge database according to fuzzy logic rules. Use of the given knowledge database allows to develop an algorithm for evaluating performance of the media system with the help of MATLAB Fuzzy Logic Toolbox, which provides an opportunity to set performance targets and thus to give different scenarios of information flows management.