Fuzzy regression using least absolute deviation estimators

Authors:
Seung Hoe Choi;James J. Buckley
Affiliations:
Hankuk Aviation University, Department of General Studies, 411, Koyang, Korea;University of Alabama, Department of Mathematics, 35294, Birmingham, AL, USA
Venue:
Soft Computing - A Fusion of Foundations, Methodologies and Applications - Special issue on BISCSE 2005 " Forging the Frontiers" Part II
Year:
2007

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Abstract

In fuzzy regression, that was first proposed by Tanaka et al. (Eur J Oper Res 40:389–396, 1989; Int Cong Appl Syst Cybern 4:2933–2938, 1980; IEEE Trans SystMan Cybern 12:903–907, 1982), there is a tendency that the greater the values of independent variables, the wider the width of the estimated dependent variables. This causes a decrease in the accuracy of the fuzzy regression model constructed by the least squares method. This paper suggests the least absolute deviation estimators to construct the fuzzy regression model, and investigates the performance of the fuzzy regression models with respect to a certain errormeasure. Simulation studies and examples show that the proposed model produces less error than the fuzzy regression model studied by many authors that use the least squares method when the data contains fuzzy outliers.