Estimation of a simple linear regression model for fuzzy random variables

Authors:
Gil González-Rodríguez;Ángela Blanco;Ana Colubi;M. Asunción Lubiano
Affiliations:
Research Unit on Intelligent Data Analysis and Graphical Models, European Centre for Soft Computing, 33600 Mieres, Spain;Dpto. de Estadística e I.O. y D.M., Universidad de Oviedo, 33007 Oviedo, Spain;Dpto. de Estadística e I.O. y D.M., Universidad de Oviedo, 33007 Oviedo, Spain;Dpto. de Estadística e I.O. y D.M., Universidad de Oviedo, 33007 Oviedo, Spain
Venue:
Fuzzy Sets and Systems
Year:
2009

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Abstract

A generalized simple linear regression statistical/probabilistic model in which both input and output data can be fuzzy subsets of R^p is dealt with. The regression model is based on a fuzzy-arithmetic approach and it considers the possibility of fuzzy-valued random errors. Specifically, the least-squares estimation problem in terms of a versatile metric is addressed. The solutions are established in terms of the moments of the involved random elements by employing the concept of support function of a fuzzy set. Some considerations concerning the applicability of the model are made.