Fuzzy least-absolutes regression using shape preserving operations

The purpose of this study is to introduce a new fuzzy regression model, based on the least-absolutes method. The fuzzy simple and fuzzy multivariate regression models with fuzzy input-fuzzy output are considered in which the coefficients of the models are themselves fuzzy. The proposed method is based on a new metric on the space of LR fuzzy numbers. Fuzzy arithmetic operations are based on the weakest triangular norm, TW, which is the unique triangular norm that preserves the shape of fuzzy numbers during multiplication. The results of comparative studies and numerical examples indicate that, using the similarity measure criterion as well as a predictive ability index, the proposed method has a better performance than the least-squares method, especially when the data set includes some outlier data point(s).