BUILDING A MATHEMATICAL MODEL BASED ON ESTIMATES OF THE COMPETITIVENESS OF THE REGIONS OF THE RUSSIAN FEDERATION FOR AUTOMATION SUPPORT FOR DECISION-MAKING IN SOCIAL STRUCTURES

Abstract

The problem of constructing a mathematical model for assessing the competitiveness of the regions of the Russian Federation has been formulated and solved. For this, a structuring method based on hierarchical trees is proposed. Their leaves are statistical indicators of socio-economic activity according to official data. These indicators are combined using integral characteristics. An example of the analysis of networks of socio-economic indicators based on the construction of minimal sections of the Kolmogorov – Chapman equations for the “Innovation” indicator is given. To describe the leaf vertices of the indicator trees, it is proposed to use status functions that represent complex-valued functions. The proposed mathematical model represents a system of integrodifferential equations, including the status function for the integral indicator of the competitiveness of the region, functions for each of the integral indicators, polynomials that are obtained as a result of interpolation of statistical data, and management influences. The analysis of the obtained graphs of the normalized values of a number of static indicators, the assessment of trends is given. The possibility of using numerical methods of nonlinear dynamics based on status functions to take into account the cross-section and mutual influence of the parameters of the risks of competitiveness of the regions of the Russian Federation for use in automating decision support in social structures is shown.