Two- and three-way component models for LR fuzzy data in a possibilistic framework

In this work we address the data reduction problem for fuzzy data. In particular, following a possibilistic approach, several component models for handling two- and three-way fuzzy data sets are introduced. The two-way models are based on classical Principal Component Analysis (PCA), whereas the three-way ones on three-way generalizations of PCA, as Tucker3 and CANDECOMP/PARAFAC. The here-proposed models exploit the potentiality of the possibilistic regression. In fact, the component models for fuzzy data can be seen as particular regression analyses between a set of observed fuzzy variables (response variables) and a set of unobservable crisp variables (explanatory variables). In order to show how the models work, the results of an application to a three-way fuzzy data set are illustrated.