A fuzzy robust regression approach applied to bedload transport data

ABSTRACT

Fuzzy least-square regression can be very sensitive to unusual data (e.g., outliers). In this article, we describe how to fit an alternative robust-regression estimator in fuzzy environment, which attempts to identify and ignore unusual data. The proposed approach concerns classical robust regression and estimation methods that are insensitive to outliers. In this regard, based on the least trimmed square estimation method, an estimation procedure is proposed for determining the coefficients of the fuzzy regression model for crisp input-fuzzy output data. The investigated fuzzy regression model is applied to bedload transport data forecasting suspended load by discharge based on a real world data. The accuracy of the proposed method is compared with the well-known fuzzy least-square regression model. The comparison results reveal that the fuzzy robust regression model performs better than the other models in suspended load estimation for the particular dataset. This comparison is done based on a similarity measure between fuzzy sets. The proposed model is general and can be used for modeling natural phenomena whose available observations are reported as imprecise rather than crisp.

KEYWORDS:

• Fuzzy outlier data
• Fuzzy robust regression
• Goodness of fit
• Least trimmed squares
• Robust regression
• Similarity measure

MATHEMATICS SUBJECT CLASSIFICATION:

• Primary 62G08
• 62J86
• Secondary 62J05

Acknowledgments

This research was supported by Research Council of Semnan University. The authors thank the anonymous referees and Editor-in-Chief, Professor Balakrishnan.