Disparities in the development of regions in any country affect the entire national economy. Detecting the disparities can help formulate the proper economic policies for each region by taking action against the factors that slow down the economic growth. This study was conducted with the aim of applying clustering methods to analyse regional disparities based on the economic development indicators of the regions of Ukraine. There were considered fuzzy clustering methods, which generalize partition clustering methods by allowing objects to be partially classified into more than one cluster. Fuzzy clustering technique was applied using R packages to the data sets with the statistic indicators concerned to the economic activities in all administrative regions of Ukraine in 2017. Sets of development indicators for different sectors of economic activity, such as industry, agriculture, construction and services, were reviewed and analysed. The study showed that the regional cluster classification results strongly depend on the input development indicators and the clustering technique used for this purpose. Consideration of different partitions into fuzzy clusters opens up new opportunities in developing recommendations on how to differentiate economic policies in order to achieve maximum growth for the regions and the entire country.

Formation of regional development strategies is impossible without taking into account the disparities in the development levels of regions which affect the entire national economy. Strengths and weaknesses of the functioning of each regional economic system, favourable and negative trends in the development of regions, disparities in the development levels, should be analysed and detected. This paper is devoted to applying of fuzzy clustering methods for the purpose of differentiation of development levels of the regions of Ukraine, in order to make recommendations on using of fuzzy clustering results in shaping regional development strategies. The fuzzy clustering methods were applied to the regional economic development indicators of the regions of Ukraine in 2017. There were considered different fuzzy clustering results and clustering validity techniques. The study presents the fuzzy classifications accompanied with the cluster validity process and substantial analysis of the economic indicators. The results of fuzzy clustering allow to consider in more detail the similarities in the regional economic development levels, assigned to the same clusters, and reveal the dissimilarities between the regions assigned to the different clusters. The membership coefficients can be used as values for regulation of influence on important economic components of the regional development strategies.

To ensure the sustainable development of an enterprise, it is necessary to properly analyze the enterprise development, to ground the plans and management decisions on effective diagnostics and prediction of current and future economic situation at the enterprise. The article presents a study on the application of fuzzy time series forecasting methods. A new approach is applied to forecasting an enterprise's net income using a fuzzy technique. For testing the methodology, there were used statistical data on the enterprise net income level of the Ukrainian enterprise from 2002 to 2017. In the method of Stevenson and Potter, it is proposed to use as the universe of discourse, in the process of applying the method for all defined fuzzy sets, the intervals of variation of such indicator as growth rate. The same background as in Stevenson and Porter’s model is used in this article for forecasting the time series levels using the growth rates of the actual data as the universe of discourse. The forecasting results, obtained by this approach, are supposed to have more accuracy rate than other fuzzy time series models. Some modifications of this technique are proposed to obtain a higher accuracy rate and a point forecast one step forward.

The level of dependence of the ecological state and its management in the Khmelnytsky region of Ukraine on the welfare of the population of this region is analyzed. The relationship between the level of income of the population of the region and the level of motivation of the same population in the sorting of buildings using a systematic approach within the ecological and economic system. The shift of consumption by the population of the region from the non-food sector to the food sector causes not only a change in parity in the triangle "man - business entity - nature", but also proves the lack of public interest in sorting household waste. This level of social responsibility and motivation of the region's population will indicate non-compliance with the goals of sustainable development of the region. The model of dependence of need for sorting of waste on the level of income of the population offered by us in article confirms it. The forecast of income growth of the population of Khmelnytsky region makes it possible to make assumptions about the growing interest of the population in sorting household waste, which will ultimately contribute to the sustainable development of the region

Many tasks in economic research are based on arithmetic calculations of indicators that reflect the state of economic development. The general incompleteness of publicly available data, designed to solve such problems, has led to the emergence of numerous decision support systems based on fuzzy arithmetic. The article presents a study on the approach aimed at integrating fuzzy information about economic indicators into economic models. The definition of arithmetic operations on fuzzy values is given, and the methods of obtaining the resulting fuzzy indicators with the help of some software tools are considered. Analytical and numerical methods of obtaining the resulting indicators in the form of fuzzy numbers are described and analyzed. A direct calculation algorithm for all arithmetic operations is proposed, utilized, and used for the evaluation of resulting indicators. Also, analytical and numerical methods for obtaining fuzzy results are considered in the article, and some of them are proposed for utilization. On the example of economic indicators used in the labor rationing, the results of an evaluation of some indicators for a technological operation in the form of fuzzy numbers were obtained by different methods and compared. The practical recommendations, given in the article, on the use of fuzzy arithmetic in decision support systems outline the directions of further research.