Symmetric fuzzy linear regression using multi-objective optimization

Abstract

Fuzzy Linear Regression (FLR) modeling and its application in different areas has been the focus of significant research in recent years. Because of the many different interpretations of fuzzy problems, diverse contributions have been made. However, they can be grouped under two categories: the least-square methods, and possibilistic approaches. In this paper, a new bi-objective goal programming model for a fuzzy linear regression problem is proposed. The proposed model considers the problem in two cases: (1) crisp independent variables, fuzzy parameters and fuzzy dependent variables, and (2) fuzzy independent variables, fuzzy parameters and fuzzy dependent variables. Then, an augmented -constraint method is applied to deal with a bi-objective optimization problem. Through comprehensive numerical examples, the proposed model is compared with state of art models from the research with respect to five performance criteria. The experimental results show the efficiency and efficacy of the model in both cases. Finally, some concluding remarks and future research directions are provided.

Keywords:

• augmented ε-constraint
• bi-objective optimization
• linear regression
• fuzzy sets
• possibilistic approach