Investigation on objective function and assessment rule in fuzzy regressions based on equality possibility, fuzzy union and intersection concepts

•Introducing novel definition to the possibility of equality of two fuzzy numbers.•Applying the novel definition into the objective function.•Developing precise method to calculate the error term between two fuzzy numbers.

Various methods have been proposed to estimate parameters of fuzzy linear regression models by possibility theory. A novel definition of the possibility of equality of two fuzzy numbers is introduced here. This novel equality of possibility is applied to objective function in the fuzzy linear regression model to obtain coefficients of the model. To evaluate the results of the model with other models, a more precise method of measuring error is developed to calculate difference between fuzzy numbers, based on the fuzzy union and intersection concepts. Several numerical examples are presented to illustrate the capability of the proposed approach in comparison to the other methods by obtaining more accurate results. Finally an application of the method is given for SAFA Rolling & Pipe Mills Company.