Robust intuitionistic fuzzy regression functions approaches

Abstract

The fuzzy regression functions approach is a fuzzy inference system that is not rule-based and not based on expert knowledge, unlike classical fuzzy inference systems. The fuzzy regression functions approach can be defined as a fuzzy inference system based on regression analysis using the ordinary least squares method and fuzzy clustering method. As is known, the ordinary least squares method is not effective when there is an outlier in the data set. So, the fuzzy regression functions approach is affected by the outliers. Since the fuzzy regression functions approach is affected by the outlier in the data set, it is inevitable that the intuitionistic fuzzy regression functions approach, which is a generalization of the fuzzy regression functions approach, is also affected by the outliers in the data set. In this study, robust intuitionistic fuzzy regression function approaches that are not affected by the outliers in the data set are proposed. In the proposed approach, the parameter estimation is made using the robust regression-based Welsch, Bisquare, Talwar, Huber, Logistic, and Cauchy functions instead of the ordinary least squares method. The performance of the proposed method is evaluated over Bitcoin and gold time series in different years. The analysis step is carried out separately for the original case of the relevant time series and for the case where they contain outliers. As a result of the analysis, it is concluded that the proposed method gives successful forecasting results both for the case where the time series contains outliers and for the original case. According to the statistical test results, the proposed method creates a statistically significant difference compared to other methods when the data contains outliers.