Abstract
The paper is devoted to the construction of a fuzzy regression model, the input and output data of which are Z-numbers. The coefficients of the regression model are crisp numbers. The definition of Z-number was proposed by prof. Lotfi Zadeh in 2011 for fuzzy information processing, the reliability of which is also fuzzy measured. In the paper the both components of Z-numbers are values of linguistic variables with the properties of completeness and orthogonality. Operations on Z-numbers are based not on classical fuzzy arithmetic, but on weighted fuzzy arithmetic, which greatly simplifies the operation, but at the same time, the original information features are preserved. The incoming information is formalized using weighted segments, based on which the distance between the initial and model data is determined. The optimization problem is solved with the condition of a minimum sum of squares of these distances, which allows to obtain unknown coefficients of the regression model.
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