Fuzzy Quantile Linear Regression Model Adopted with a Semi-Parametric Technique based on Fuzzy Predictors and Fuzzy Responses

Abstract

As an extension to statistical techniques, fuzzy regression analysis estimates the relationship between fuzzy independent variables and non-fuzzy and/or fuzzy dependent variables. However, facing skewed or non-normal data may lead to vague results if the conventional least square models are used. However, there are many situations in applications of intelligence systems where regression components are fuzzy quantities instead of exact values. The present work is aimed to propose a fuzzy semi-parametric quantile regression model with fuzzy predictors, a fuzzy smooth function, exact coefficients and fuzzy responses. The proposed method is based on a new class of novel kernel-based signed-distance measures in space of fuzzy numbers. Main features of the proposed signed-distance including its robustness were studied. It was shown that the proposed signed-distance measure is more reasonable and effective than a common signed-distance which extensively has been used in fuzzy set theory. This is the reason why we decided to apply the proposed signed-distance to extend the classical quantile regression model. Then, a hybrid algorithm was suggested to evaluate optimal bandwidth, non-fuzzy regression coefficients and fuzzy smooth function at a specific quantile level. The proposed method was then compared with some common fuzzy regression models based on two data sets including a simulation study and an applied example. The numerical results clearly indicated that the proposed fuzzy semi-parametric quantile linear regression model performs better than the other available methods in terms of some common goodness-of-fit criteria in cases where the data set includes skewness and/or some outlier data point. The main advantages of the proposed method are as follows: 1-it is not so sensitive to the outlier data points and/or skewed data, 2- it possesses better fitting effect compared to other existing fuzzy regression models. Thus, the proposed quantile regression model could be successfully applied in many practical studies of fuzzy regression model in real-world applications.