A novel fuzzy linear regression model based on a non-equality possibility index and optimum uncertainty

Various kinds of fuzzy regression models are introduced in the literature and many different methods are proposed to estimate fuzzy parameters of the models. In this study, a new approach is introduced to find the parameters of a linear fuzzy regression, with fuzzy outputs, the input data of which is measured by crisp numbers. Based on a non-equality possibility index, a new objective function is designed and solved, by which a minimum degree of acceptable uncertainty (the h-level or h-cut) is found. Four numerical examples are presented to compare the proposed approach with some other methods. Results show superiority of the new approach based on the criterion used by Kim and Bishu in the cases studied here. A realistic application of the proposed method is also presented, by which the total energy consumption of the Residential-Commercial sector in Iran is modeled using three variables of the GDP, number of the Households and an Energy Price index as inputs (exogenous variables) to the model.