Document Type : Original Article
Authors
1 Department of Statistics, SR.C., Islamic Azad University, Tehran, Iran
2 Department of Statistics, Faculty of Matmatical sciences, Uiversity of Gulian, Rasht, Iran
3 Department of Industrial Engineering, Faculty of Technology and Engineering East of Guilan, University of Guilan RudsarVajargah, Guilan, Iran
Abstract
This paper compares symmetrical and asymmetrical triangular fuzzy numbers (TFNs) in fuzzy linear regression (FLR), focusing on how their structural differences impact uncertainty representation, parameter estimation, and predictive accuracy. Symmetrical TFNs are popular for their simplicity and computational efficiency, but assume balanced uncertainty an assumption often unrealistic in real systems with skewed or one-sided variability. Asymmetrical TFNs overcome this by allowing different left and right spreads, offering finer modeling of directional uncertainty.
Applied to a numerical dataset with right-skewed uncertainty, the asymmetrical TFN model significantly outperforms the symmetrical one, reducing the average fuzzy Euclidean distance by about 50% (from 1.54 to 0.78) and improving all other evaluation metrics. Visual analysis shows asymmetrical TFNs adaptively widen prediction bands at higher inputs, capturing the data’s inherent skew unachievable with symmetrical TFNs.
While symmetrical TFNs work well for balanced, low-variability cases, asymmetrical TFNs provide a more realistic and flexible framework for modeling directional uncertainty in engineering, environmental, economic, and decision-support applications. This study guides TFN selection in FLR and underscores the importance of asymmetry where uncertainty is non-uniform or skewed.
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