Robust fuzzy regression functions approaches

Abstract

In the structure of fuzzy inference systems, the decision-making process is based on certain rules called “if-then”. It is highly difficult to determine these rules. The fuzzy regression functions approach proposed to overcome this difficulty is a fuzzy inference system method based on fuzzy set theory and multiple regression analysis. Even though the fuzzy regression functions approach gives successful forecasting results, its performance is affected by the outliers in the data set. In this study, the parameter estimations of regression functions are obtained by robust regression based on Andrews, Bisquare, Talwar, Huber, Fair, Logistic and Cauchy functions. Thus, the forecasting performance of the proposed method is not affected even if the data set contains an outlier. The forecasting performance of the proposed method, with and without the data set containing an outlier, is compared with many forecasting methods in the literature. Its superior forecasting performance is supported by the analysis results. It is seen that the proposed method has a superior forecasting performance.