Z-Regression for Аnalysis and Reliable Prediction of Qualitative Characteristics

A regression model under Z-information has developed in the paper. The initial information for constructing the model is linguistic Z-numbers, defined on the unit segment. For a Z-number, an interval type-2 fuzzy number is defined, using aggregating characteristics of reliability (second component of Z-number). To do this, the aggregating segment of reliability and its middle are use. In the paper was made a choice in favor of transforming Z-numbers into type-2 fuzzy numbers, since Z-numbers are closer in structure to them than to type-1 fuzzy numbers, which, however, are most often used to transform Z-numbers and construct different models. Input and output interval type-2 fuzzy numbers are determined for the initial Z-numbers. The optimization function is defined as the sum of squares for the differences between parameters of output type-2 fuzzy numbers and the model type-2 fuzzy numbers. To determine the unknown regression coefficients, the minimum of the optimization function was found using known methods. Reliability recognition of model output information has developed.