International Scientific Journals
of Scientific Technical Union of Mechanical Engineering "Industry 4.0"

As result of the analysis of the structure and consistency of the national security and cybersecurity in the national legislation the authors reach the conclusion that the national security in Bulgaria is government function and has system character in line with the complex system theory. The national security system together with the cybersecurity system have fully functionality of the complex system because beside structure, interaction and relations, the system feedbacks, as periodic reports and document review procedures that reshapes the links and relations. The processes of: control as a cycle, security risk management and capability planning are reflected in the national legislation and are prescriptive, as well.

The decision making is based on the objective preferences and starting from this position the incorporation of human preferences in complex systems is a contemporary trend in scientific investigations. In Complex system where a human participation is decisive for the final decision the human thinking, notions and preferences have cardinal significance and need analytical representation. Mathematical modeling of complex „human – process” systems and build mathematically well-founded control solution need analytical representation of quantitative information like preferences. This could be made by utility theory and stochastic approximation theory. The objective of the paper is to present a strict logical mathematical approach for modeling and estimation of human preferences as machine learning in the process of building of mathematical models of complex systems with human participation. The approach is demonstrated on a case study in the area of risk portfolios optimization and financial risk management with color noise. The objective of the paper is to present a mathematical approach for modeling and estimation of human preferences as machine learning in the process of building of mathematical models of complex systems with human participation.