This study attempts to develop a quasi type-2 fuzzy regression model in full quasi type-2 fuzzy environment. To estimate the parameters of the proposed model, first, a weighted distance between quasi type-2 fuzzy numbers is defined based on L1-norm. Then some approximations for multiplication of two quasi type-2 fuzzy numbers (QT2FNs) are introduced. The problem of estimation of the parameters relies on a non-linear optimization problem, which is converted to a linear optimization problem. The method can handel both symmetric and asymmetric data. Two real world examples demonstrate the feasibility and efficiency of the proposed method. The predictive performance of the model is examined by cross-validation, and a similarity measure is used to compare our model with a similar model.
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