Abstract
The goal of the paper is to develop a regression model under the initial Z-information based on an alternative method to the least squares method, and free from the assumptions regarding probability distributions of initial data. Formalization of input and output information is carried out on the basis of Z-numbers and linguistic variables, followed by the construction of a multidimensional quintile regression model with fuzzy coefficients. The optimization function is defined as the sum of the loss functions for the differences between the weighted output fuzzy numbers and the weighted model fuzzy numbers. To determine the parameters of the unknown regression coefficients, a linear programming problem is solved to find the minimum of the optimization function. The developed Z-regression is free from the shortcomings of existing models and provides new opportunities for solving tasks in problem areas with the active participation of experts, taking into account the reliability of information received from them.