Fuzzy Regression Analysis using Trapezoidal Fuzzy Numbers

Abstract

As a widely used method, regression analysis plays an increasingly important role in creating statistical models and making forecasts in the field of economics and finance. The use of traditional regression for modeling socio-economic processes is not sufficiently substantiated in some situations. Currently, a new direction is being actively developed, associated with fuzzy regression analysis and its application as an alternative to classical methods for modeling economic phenomena. Fuzzy regression methods are based on the theory of fuzzy sets. A number of methods and their modifications are proposed for constructing fuzzy regression models, but most of them use triangular fuzzy symmetric numbers. In this paper, we propose a new method for constructing linear fuzzy regression using trapezoidal fuzzy numbers. The method is based on dividing the sample using a regression model which is estimated by using the ordinary least squares. Two fuzzy regressions using triangular numbers are estimated from the formed samples, on the basis of which a fuzzy model with trapezoidal fuzzy numbers is constructed. Basing on the proposed method, a linear fuzzy model of the gross regional product as an indicator of the economic development of the Republic of Tatarstan of Russia is constructed depending on a number of factors. A comparative assessment of the quality of fuzzy regression models using triangular and trapezoidal numbers was performed.