Models of Fuzzy Linear Regression: An Application in Engineering

The classical Linear Regression is an approximation for the creation of a model which connects a dependent variable y with one or more independent variables X, and it is subjected to some assumptions. The violation of these assumptions can influence negatively the power of the use of statistical regression and its quality. Nowadays, to exceed this problem, a new method has been introduced, and is in use, that is called fuzzy regression. Fuzzy regression is considered to be possibilistic, with the distribution function of the possibility to be connected with the membership function of fuzzy numbers. In this article, we examine three models of fuzzy regression, for confidence level h=0, for the case of crisp input values, fuzzy output values and fuzzy regression parameters, with an application to Hydrology, in two rainfall stations in Northern Greece.