Modelos de regressão Fuzzy

Abstract

In many practical situations, we are interested in modeling the functional relationship between a response variable and one or more explanatory variables, for which we can use the regression models. Those models have certain assumptions, which when violated can generate certain undesired characteristics in the model. For this reason, several diagnostic methodologies, as well more robust models, or with more flexible assumptions have been proposed in recent years. Fuzzy sets theory, on the other hand, which has gained attention since the work of Zadeh (1965, Information and control), and has been used in numerous applications in which there are uncertainty factors associated with the pertinence of elements to their respective sets. Methodologies based on fuzzy theory have been used for classi cation mechanisms, decision-making systems, arti cial intelligence, etc. In this paper we first present the fuzzy set theory and later on we introduce two models of fuzzy regression, one based on the proposal of Yen et. al. (1999), Fuzzy Sets and Systems, and another based on Ishibushi and Nii (2001, Fuzzy Sets and Systems), the latter being hybrid, in the sense that it uses the usual least-squares estimators to estimate part of the model parameters. The assumptions of this methodology are more flexible than the usual linear regression model, since we do not need to assume a particular distribution about the source of variation. In order to compare the results of these two models with the usual linear regression model, we present two case studies.