Sequential Extraction of Fuzzy Regression Models: Least Squares and Least absolute Deviations

Fuzzy c-regression models are known to be useful in real applications, but there are two drawbacks: strong dependency on the predefined number of clusters and sensitiveness against outliers or noises. To avoid these drawbacks, we propose sequential fuzzy regression models based on least absolute deviations which we call SFCRMLAD. This algorithm sequentially extracts one cluster at a time using a method of noise-detection, enabling the automatic determination of clusters and having robustness to noises. We compare this method with the ordinary fuzzy c-regression models based on least squares, fuzzy c-regression models based on least absolute deviations, and moreover sequential fuzzy regression models based on least squares. For this purpose we use a two-dimensional illustrative example whereby characteristics of the four methods are made clear. Moreover a simpler and more efficient algorithm of SFCRMLAD can be used for scalar input and output variables, while a general algorithm of SFCRMLAD uses linear programming solutions for multivariable input. By using the above example, we compare efficiency of different algorithms.