Parameter Estimation of the Engel Curve using the Method of Fuzzy Regression to Assess the Level of Welfare in the Republic of Tatarstan

This article proposes the estimating method of a quality indicator of “population welfare in the region” based on the theory of fuzzy sets. For welfare analysis there are estimated the parameters of Engel curves using the method of fuzzy regression. The resulting model parameters are triangular fuzzy numbers whose cofactor is the fuzzy evaluation of the welfare population in the region. For defazzification of obtained fuzzy number, there is calculated the area of the intersection of fuzzy numbers of the actual wealth level and the possible linguistic terms from “absolute poverty” to “a high level of well-being”. These obtained results suggest that the population of the Republic of Tatarstan has a good and a high level of well-being. The proposed methodology provides an analysis on the short time series and takes account of incomplete or inaccurate information.