ON THEIL'S METHOD IN FUZZY LINEAR REGRESSION MODELS

Abstract. Regression analysis is an analyzing method of regressionmodel to explain the statistical relationship between explanatory variableand response variables. This paper propose a fuzzy regression analysisapplying Theils method which is not sensitive to outliers. This methoduse medians of rate of increment based on randomly chosen pairs of eachcomponents of -level sets of fuzzy data in order to estimate the coe-cients of fuzzy regression model. An example and two simulation resultsare given to show fuzzy Theils estimator is more robust than the fuzzyleast squares estimator. One of the central objectives of mathematics is to interpret natural or so-cial phenomena with mathematical tools including numbers, signs, and axioms.Uncertainties may occur during the process of transforming a natural or socialphenomenon into a mathematical problem. These uncertainties involve twodistinctive types: stochastic uncertainty whose uncertainty can be naturallyresolved as time passes, and fuzzy uncertainty whose uncertainty cannot beresolved even with the passage of time. Of the two types of uncertainties,the study on stochastic uncertainty is particularly active that it is now ap-plied in numerous elds. Zadeh introduced fuzzy theory in explaining fuzzyuncertainty with respect to ambiguity and vagueness. He further applied thistheory to establish a necessary system for handling information expressed insuch ambiguous or vague manners ([18], [19]).Tanaka established fuzzy regression model as an attempt to explicate therelationship among variables that are ambiguously or vaguely presented ([15],[16]). Fuzzy regression model can be classi ed into two categories depending onthe response function which may be known or unknown. In this case, the formerand latter are called parametric model and non-parametric model, respectively.In addition, the method to estimate the fuzzy regression model can be classi- ed into two kinds methods in terms of minimization. One is the numericalmethod which minimize the sum of spreads of estimated fuzzy numbers, the