Methodology for Determining the Limit Values of National Security Indicators Using Artificial Intelligence Methods

Applying artificial intelligence methods, the paper frames the algorithm structure and software for the formalized determination of the type of distribution (automatic classification) of the probability density function and the vector of limit values by justifying theoretically security gradations and determining quantitatively security indicators. The methodological basis of the research is the applied systems theory, statistical analysis, and methods of artificial intelligence (cluster analysis). The study of the approaches applied showed the absence of a theoretical basis for determining security gradations and the absence of their theoretical quantitative justification. The theoretical basis for determining security gradations is the concept of an extended "homeostatic plateau", which connects three levels of security in both directions: optimal, crisis, and critical with spheres of positive, neutral and negative feedback. To determine the bifurcation points (vector of limit values), the “t-criterion†method is used, which consists in constructing the probability density function of a “benchmark†sample, determining whether it belongs to the type of distribution with the calculation of statistical characteristics (mathematical expectation, mean square deviation, and asymmetry coefficient) and formalized calculation of the vector of limit values for characteristic types of distribution (normal, lognormal, exponential). To solve the problem of recognising (automatic classifying) the type of distribution of probability density functions of security indicators, artificial intelligence methods are used, namely, a discriminant method from the class of cluster analysis methods using quantitative and qualitative metrics: Euclidean distance, Manhattan metric and recognition by characteristic features. To digitize the determination of the vector of safety indicators limit values, an algorithm structure and software in the C++ programming language (version 6) have been developed, which ensures full automation of all stages of the algorithm and the adequacy of recognising graphic digital data with a predetermined number of clusters (types of distribution). A distinctive feature of the proposed method of formalized determination of the security indicators limit values is a complete absence of subjectivity and complete mathematical formalization, which significantly increases the speed, quality and reliability of the results obtained when evaluating the level of sustainable development, economic security, national security or national stability, regardless of the level of a researcher's qualification.