Fuzzy Stochastic Automation Model for Decision Support in the Process Inter-Budgetary Regulation

The purpose of this article is to study the theoretical foundations of the concept of fiscal decentralization, as the main path of self-development of the national economy of any country, and to develop mathematical tools that support decision-making in the aspect of “hard” budget constraints. The study of the problems of fiscal policy formation in foreign countries presented in modern scientific literature has revealed that the degree of application of the concepts of “soft” and “hard” budget restrictions is an actual topic in the theory of fiscal federalism. It has been substantiated that decision-making within the framework of “soft” budget constraints (financial assistance) leads to low tax autonomy of territories and limited liability of regional and municipal authorities for the results of their financial policy. As a research hypothesis, we put forward the thesis that it is necessary to create conditions for encouraging subnational authorities to support the territorial economy by granting them the possibility to use part of the taxes collected in the respective territories. The implementation of this thesis has given rise to the problem of quantifying decisions made regarding the establishment of standards for the distribution of tax revenues between budgets of different levels of the hierarchy of the country’s budget system. In terms of solving this problem, the author has constructed mathematical models based on the use of synthesis of mathematical apparatus of the theory of stochastic automata, fuzzy algebra, and simulation. In terms of solving this problem, the author proposed the use of mathematical modeling methods. The article presents the results of constructing economic and mathematical models to support decision-making in the vertical distribution of tax revenues between budgets. The models include stochastic automata, as mathematical abstractions, describing the expedient behavior of an economic agent when choosing management alternatives for territories of different levels of economic development. The transition functions of automaton models are formally described on the basis of the synthesis of mathematical apparatus of the theories of stochastic automata operating in random environments and fuzzy sets. The expediency property of the behavior of automaton models is justified by proving the corresponding theorems. The random environment in which stochastic automata are immersed is formed by a simulation model. The article demonstrates the results of experiments carried out on models, as well as a conceptual scheme of interaction between the automaton and simulation models.