A. V. Chechkin - Professor, Military Academy named after Peter the Great. E-mail: A.Chechkin@mail.ru
M. V. Pirogov - Head of Sector, NGO named after S.A. Lavochkin. E-mail: pmv_mvp@mail.ru

Fundamentals of mathematical method of certification systems are considered. The method is based on the special formalism of complex systems (critical systems). Certification is a way to control goods and services. Certification is extremely important in the current conditions, it is necessary and should be mandatory. The certification process should cover all phases of the life cycle of the system. In the process of the synthesis of the system must be certified by all of the relevant components of all hierarchical levels of the system. In this evaluation, comparison and choice of components for their application in the system should be carried out. And, of course, must be certified system as a whole. All this requires are not fragmented, as in the present time, but full of formalization and informatization of the problem area of complex systems. Moreover, we need intellectualization of systems, which is understood the ability to solve not only standard, but also non-standard tasks. As the basis of such an approach to certification, we offer specialized formalism of complex systems. This is the formalism of schemes of radicals, based on the concept of the environment of radicals, offered by A.V. Chechkin. According to this concept, a radical is a functional system, which has to status, available from the outside. It has passive and active state. Environment of radicals is the set of radicals, connected among themselves. System (certified) should serve its purpose that is to ensure the achievement of targeted schemes, while avoiding conflicts. In the general case the conflicts can be, either standard or not. Schemes, which are intended for the decision of tasks of certification and resolution of conflicts in the process of achieving the target schemes of radicals, are considered. There is also a brief description of the developed method of the synthesis of certified radicals, the decision of standard and non-standard tasks of life cycle of the system in the environment of the radicals.