Models and methods of regression analysis under conditions of fuzzy initial data

Abstract

The paper considers the problem of regression analysis with indeterminate explanatory and explained variables. A quality criterion for estimating the regression coefficients is formulated and justified, taking into account possible significant differences in the accuracy of assigning different variables. The study considers a method of calculating the regression coefficients in accordance with the concept of least squares. The proposed approach provides a reasonable compromise between the conflicting requirements: the maximum compactness of the fuzzy value function of the explained variable and the minimal deviation of the solution from the modal one. The problem is solved by minimizing the complex criterion, the terms of which determine the level of satisfaction of these requirements. An additional advantage of the approach is that the original problem, fuzzy by the nature of the initial data, is reduced to solving two usual problems of mathematical programming. The problem of fuzzy comparator identification is considered when the values of the explained variable are not defined but can be ranked by the descending of any chosen indicator. To solve this problem, the study proposes a method for estimating regression coefficients based on solving a fuzzy system of linear algebraic equations.