Document Type : Original Article

Author

• Behrouz Fathi-Vajargah

Department of Statistics, University of Guilan

Abstract

This paper presents an enhanced comparative analysis between symmetrical and asymmetrical triangular fuzzy numbers (TFNs) in fuzzy linear regression (FLR), emphasizing their influence on uncertainty modeling and prediction accuracy. While symmetrical TFNs simplify computation by assuming equal left and right spreads, they often fail to represent skewed or directional uncertainty commonly present in engineering and economic datasets. In contrast, asymmetrical TFNs introduce greater flexibility by allowing distinct spreads, thereby improving approximation accuracy. A numerical study demonstrates that the asymmetrical TFN model achieves approximately a 50% reduction in average fuzzy Euclidean distance (from 1.54 to 0.78) compared with the symmetrical model. This finding highlights that asymmetrical TFNs capture real-world uncertainty more effectively while maintaining interpretability. The results confirm the superiority of asymmetrical fuzzy modeling in scenarios involving asymmetric uncertainty, despite the associated computational complexity.

Keywords

• Fuzzy linear regression
• asymmetrical triangular fuzzy number
• symmetrical triangular fuzzy number
• uncertainty modeling
• fuzzy arithmetic