A WEIGHTED GOAL PROGRAMMING APPROACH TO FUZZY LINEAR REGRESSION WITH QUASI TYPE-2 FUZZY INPUT-OUTPUT DATA

E.HOSSEINZADEH, H.HASSANPOUR, M.AREFI, M.AMAN

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Abstract

This study attempts to develop a regression model when both input data and output data are quasi type-2 fuzzy numbers. To estimate the crisp parameters of the regression model, a linear programming model is proposed based on goal programming. To handle the outlier problem, an omission approach is proposed. This approach examines the behavior of value changes in the objective function of proposed model when observations are omitted. In order to illustrate the proposed model, some numerical examples are presented. The applicability of the proposed method is tested on a real data set on soil science. The predictive performance of the model is examined by cross-validation.

Keywords

fuzzy linear regression, goal programming, type-2 fuzzy set, uncertainty, quasi type-2 fuzzy number.