On Fuzzy Regression Adapting Partial Least Squares

Alper BASARAN
Biagio SIMONETTI
Luigi D’AMBRA

Keywords

Fuzzy regression, partial least squares, fuzzy number

Abstract

Partial Least Squared (PLS) regression is a model linking a dependent variable y to a set of X (numerical or categorical) explanatory variables. It can be obtained as a series of simple and multiple regressions of simple and multiple regressions. PLS is an alternative to classical regression model when there are many variables or the variables are correlated. On the other hand, an alternative method to regression in order to model data has been studied is called Fuzzy Linear Regression (FLR). FLR is one of the modelling techniques based on fuzzy set theory. It is applied to many diversified areas such as engineering, biology, finance and so on. Development of FLR follows mainly two paths. One of which depends on improving the parameter estimation methods. This enables to compute more reliable and more accurate parameter estimation in fuzzy setting. Second of which is related to applying these methods to data, which usually do not follow strict assumptions. The application point of view of FLR has not been examined widely except outlier case. For example, it has not been widely examined how FLR behaves under the multivariate case. To overcome such a problem in classic setting, one of the methods that are practically useful is PLS. In this paper, FLR is examined based on application point of view when it has several explanatory variables by adapting PLS.