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In this work, we focus on two things: First, in addition to the data measurement uncertainty, we develop a novel probabilistic model by imposing the additive noise in the classical fuzzy regression model. We obtain the baseline LS estimation as the maximum likelihood estimation for regression parameters. Moreover, by assuming the heavy tail distribution and by introducing the Huber norm instead of square in the cost function, we obtain more general robust fuzzy M-estimator, much more suitable for modeling the outliers often present in the data sets. © 2019 University of Belgrade.