Building a system of dynamic norms for evaluating the functioning of complex systems on the example of the regions of the Central Federal District

In this paper, we present a method of forming norms for evaluating the results of the functioning of complex systems applicable to socio-ecological and economic systems, taking into account the priorities of the development of the regions of the Russian Federation. The methodology involves the selection of normative values from a set of norms based on two methods: the first is based on the construction of econometric models using statistical data for a set of subjects (the first type) and for one selected subject (the second type). The second method uses the methodology of Bayesian intelligent measurements based on the regularizing Bayesian approach (the third and fourth types). Depending on the result of the calculations, a norm is selected that gives a higher (in the case of high priority), average (in the case of medium priority) and lower (in the case of low priority) normative value of the evaluated effective features characterizing the development of the subject. The implementation of the method is demonstrated by the example of the regions of the Central Federal District, including the Tula Region, for which econometric and fuzzy models of the relationship between the volume of gross regional product with the value of fixed assets and the number of employees for sections A (Agriculture, forestry, hunting, fishing and fish farming) and C (Mining) according to OKVED1 are constructed, forming the raw materials sector according to data for 2007–2022. The EFRA and Infoanalyst 2.0 software platforms are used as tools. The results obtained can be used by regional authorities in the formation of norms to assess the results of the functioning of the regions in the short and medium term. The study was carried out at the expense of a grant from the Russian science Foundation № 24-28-20020 and Tula Region.