Abstract <p>This article is devoted to the development of the mathematical apparatus of fuzzy cognitive modeling in the direction of methods for identifying Silov’s fuzzy cognitive maps. The problem of identifying the structure and parameters of a fuzzy cognitive map and existing methods for solving it are considered. The problems and limitations of the identification methods used are indicated and the relevance of developing a new approach is substantiated, free from identified problems and limitations. Within the framework of the proposed approach, the identification problem is reduced to the problem of optimizing a certain compliance function. To obtain the compliance function, models of formalized accounting of expert and statistical data on the simulated system are proposed based on the introduced concept of a rule. The components of the genetic algorithm used to solve the given optimization problem are described. An example of the application of elements of the new approach is considered and the main directions for its further development are indicated.</p>