A multi-objective evolutionary approach for fuzzy regression analysis

Abstract

Fuzzy regression analysis was extensively used in previous studies to model the relationships between dependent and independent variables in a fuzzy environment. Various approaches have been proposed to perform fuzzy regression analysis with most of the approaches adopting a single objective function in the generation of fuzzy regression models. Some previous studies attempted to generate fuzzy regression models using a multi-objective optimization approach in order to improve the prediction accuracy of the generated fuzzy regression models. However, in the studies, the subjective judgments of parameter settings are required for solving multi-objective optimization problems and a complete representation of Parato optimal solutions cannot be generated in a single run. To address the limitations, a multi-objective evolutionary approach to fuzzy regression analysis is proposed in this paper. In the proposed approach, a multi-objective optimization problem is formulated which involves three objectives; minimizing the fuzziness of fuzzy outputs, minimizing the effect of outliers and minimizing the mean absolute percentage error of modeling. A non-dominated sorting genetic algorithm-α is introduced to solve the problem and generate a set of Pareto optimal solutions. Finally, a technique for order of preference by similarity to ideal solution is applied to determine a final optimal solution by which a fuzzy regression model can be generated. A case study is conducted to illustrate the proposed approach. Sixteen validation tests are conducted to evaluate the effectiveness of the proposed approach. The results of the validation tests show that the proposed approach outperforms Tanaka's fuzzy regression, Peters’ fuzzy regression, compromise programming based multi-objective fuzzy regression, fuzzy least-squares regression and probabilistic fuzzy regression approaches in terms of training errors and prediction accuracy.