Poverty is still a current social issue in Poland and other countries. Due to the lack of one universally accepted definition of poverty, there are many ways to identify and measure poverty. In addition to the classic approach to identifying poor units, a fuzzy approach is also used. The aim of the article is to analyze the problem of monetary poverty in Poland in the IFR (Integrated, Fuzzy and Relative) approach using data from the Household Budget Survey, in which the risk of poverty is assessed on the basis of the cumulative distribution function of the income or expenditure and the value of Lorenz’s function. In the article, these two functions were determined on the basis of one of the theoretical distributions (the Dagum distribution). This approach allowed for the estimation of the parameters of the conditional theoretical distribution due to the characteristics of households. This provided the opportunity to determine the factors determining the risk of poverty in Poland