Two Robust Fuzzy Regression Models and Their Applications in Predicting Imperfections of Cotton Yarn

Using the generalized Hausdorff-metric, two least-absolutes (LA) approaches to multiple fuzzy regression modeling are introduced for the case of crisp input-fuzzy output data. The main advantage of the proposed models is that they are not so sensitive to the outlier data points. The proposed models as well as two common fuzzy least-squares (LS) models are employed in a case study to estimate imperfections of cotton yarn using fiber properties in a reallife data. In order to derive the fuzzy regression models between imperfections of cotton yarn and fiber properties, first, effective variables are selected by the statistical stepwise test. Then, four fuzzy models, including two new LA models and two LS models, are sought to fit the data set.
Finally, two criteria are employed to evaluate the goodness-of-fit of models. Moreover, a predictive ability index is introduced and employed to evaluate the predictability of the models. Using these criteria, a comparative study between the proposed fuzzy least-absolutes regression models and fuzzy least-squares regression models has also been addressed. The comparison results reveal that the LA-fuzzy models perform better than the LS-fuzzy models in imperfections of cotton yarn estimation for the particular data set used in this study.