In order to study the theoretical foundations and applied problems of predicting man-made damage to the national economy and methods of management at the state level in paper there is summarizes the theoretical foundations of the application of fuzzy sets as an effective mathematical tool under conditions of incomplete information and uncertainty of the future. According to the allocation of tasks in the conceptual model features a fuzzy expert system to establish interdependencies between the amount of pollution (emissions, effluents, waste) and deterioration of health of Ukraine, as well as building prediction models of man-made damage to the national economy and its verification by the example of the set interdependence between the amount of discharges (drained polluted waters without treatment), and emissions of sulfur dioxide and nitric oxide and the number of newly registered tumors in Ukraine returned the following results.
Model of fuzzy expert system for establishing interdependencies between the amount of pollution (emissions, effluents, waste) and deterioration of health of Ukraine shall include a knowledge base with 27 logical statements such as "if - then otherwise".
The model prediction of man-made damage to the national economy and established its compliance with established interdependence between the amount of discharges (drained polluted waters without treatment), and emissions of sulfur dioxide and nitric oxide and the number of newly registered tumors in Ukraine. It was established that the impact of emissions and discharges of pollutants into the incidence is cumulative in nature and appears to the time delay, because the relationship between the results must include the time lag and indicators should be averaged over a specified period of time hence volume effects.