An amalgamation of crisp and fuzzy quantile regression model.

Fuzzy set theory is the most powerful tool to describe the process of uncertainty which exist in real world and fuzzy regression is an important research topic which can be used for prediction by establishing the functional relationship between fuzzy variables. Quantile regression is also a significant statistical method for estimating and drawing inferences about conditional quantile functions. This study introduced the idea of quantile regression with respect to fuzzy. The ordinary fuzzy regression is based on least square method but here we have introduced the idea of weighted least absolute deviation method in fuzzy regression. We have considered two different cases for the illustration of our proposed technique, firstly when the input and output are taken as fuzzy and secondly, the input and output are taken as fuzzy but the parameters are crisp. The algorithm for each case is based on linear programming problem (LPP). The LPP is constructed for individual case and solved it by the method of Simplex procedure. The proposed work is then compared with the conventional fuzzy regression by using AIC criterion. Empirical study shows that the proposed technique works best in every situation where the fuzzy regression fails and also provide the results in depth. [ABSTRACT FROM AUTHOR]