A multi-attribute assessment of fuzzy regression models

Most of the fuzzy regression approaches proposed in the literature adopted a single objective function in the generation of fuzzy regression models. These approaches mostly being criticized by their weak performances analysis and their sensitivity to outliers. Therefore, this paper develops a new multi-objective two-stage optimization and decision technique for fuzzy regression modeling problems in order to handle both of the criticisms. To handle the outlier problems, in the first stage, dynamic robust to outlier objective functions is considered in the estimation problem. The estimation problem is solved by running an algorithm which generates a set of fuzzy regression models. Then, in the next stage, we design a decision schema by employing Multi-Attribute Decision Making (MADM) problem. Here, the VIKOR method is employed as a proper means to provide a design to rank the generated fuzzy regression models by the first stage to introduce the most desirable model. We include simulation numerical results and a real-world house price problem in order to highlight the advantages of the proposed method in a comparison study. The results demonstrate the effectiveness of the proposed multi-objective optimization method to handle outlier detection problem while the prediction accuracy of the model is improved.