A fuzzy regression model based on finite fuzzy numbers and its application to real-world financial data

Different sources of imprecision and uncertainty are encountered in practical problems and, thus, many elements may need to be imprecisely observed, defined or treated. In this setting, one of the most successfully applied techniques to describe possible relationships between fuzzy variables is the regression methodology. In this paper, we introduce a fuzzy regression procedure involving a class a fuzzy numbers defined by some level sets called finite fuzzy numbers. We give a characterization of the image of a finite fuzzy number in terms of the extremes of its level sets and we present a parametric family of fuzzy semidistances between them that let us to consider a total fuzzy error of estimation (described as a fuzzy sum of squares of residuals in particular cases). The estimation process consists in finding a regression model that minimizes, in a fuzzy sense, such fuzzy error. Although spreads of finite fuzzy numbers can take some values very close to zero, which complicate the task of finding nonnegative models, the presented algorithm is able to guarantee that the predicted response is a fuzzy variable. Finally a numerical example based on fuzzy economic data of China is given to illustrate the use of the proposed method.